How do you find the local max and min for #f(x)= x^2 + 8x 12#?
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To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute theTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivativeTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 =To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of theTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the functionTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 \To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function:To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: (To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( fTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(xTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x =To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) =To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 \To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2xTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x +To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 \To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ). 2.To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ fTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivativeTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to findTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x)To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find criticalTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) =To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: (To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

SinceTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x +To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivativeTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative isTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ). 3To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positiveTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

SolveTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive,To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x \To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, theTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find theTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the criticalTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical pointTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point atTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ). To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( xTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ). 4To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x =To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ). 4.To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

DetermineTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 \To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine theTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 )To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the natureTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) correspondsTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature ofTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds toTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of theTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to aTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the criticalTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimumTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point byTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluatingTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
ThereforeTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating theTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore,To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the secondTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the localTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivativeTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimumTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative:To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occursTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: (To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs atTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( fTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at (To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( xTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(xTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x)To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 \To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) =To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 )To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) withTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with aTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 \To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a valueTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ). To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value ofTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ). 5To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of (To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ). 5.To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( fTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

SinceTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since theTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4)To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the secondTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) =To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivativeTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivative isTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (4)^To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivative is positiveTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (4)^2To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivative is positive (To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (4)^2 +To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivative is positive ( (To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (4)^2 + To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivative is positive ( ( f''(x) > To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (4)^2 + 8(4)  12 = 16 To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivative is positive ( ( f''(x) > 0To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (4)^2 + 8(4)  12 = 16  To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivative is positive ( ( f''(x) > 0 )), the criticalTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (4)^2 + 8(4)  12 = 16  32To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivative is positive ( ( f''(x) > 0 )), the critical point atTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (4)^2 + 8(4)  12 = 16  32 To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivative is positive ( ( f''(x) > 0 )), the critical point at (To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (4)^2 + 8(4)  12 = 16  32  To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivative is positive ( ( f''(x) > 0 )), the critical point at ( x =To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (4)^2 + 8(4)  12 = 16  32  12 = To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivative is positive ( ( f''(x) > 0 )), the critical point at ( x = To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (4)^2 + 8(4)  12 = 16  32  12 = 28 ).
To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivative is positive ( ( f''(x) > 0 )), the critical point at ( x = 4To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (4)^2 + 8(4)  12 = 16  32  12 = 28 ).
ThereTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivative is positive ( ( f''(x) > 0 )), the critical point at ( x = 4 \To find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (4)^2 + 8(4)  12 = 16  32  12 = 28 ).
There areTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivative is positive ( ( f''(x) > 0 )), the critical point at ( x = 4 ) correspondsTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (4)^2 + 8(4)  12 = 16  32  12 = 28 ).
There are no local maxima for this functionTo find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:

Compute the derivative of the function: ( f'(x) = 2x + 8 ).

Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).

Solve for ( x ) to find the critical point: ( x = 4 ).

Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).

Since the second derivative is positive ( ( f''(x) > 0 )), the critical point at ( x = 4 ) corresponds toTo find the local maxima and minima for ( f(x) = x^2 + 8x  12 ), follow these steps:

Find the critical points by setting the derivative equal to zero and solving for ( x ): [ f'(x) = 2x + 8 = 0 ] [ 2x = 8 ] [ x = 4 ]

Evaluate the second derivative to determine the nature of the critical point: [ f''(x) = 2 ]

Since the second derivative is positive, the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the local minimum occurs at ( x = 4 ) with a value of ( f(4) = (4)^2 + 8(4)  12 = 16  32  12 = 28 ).
There are no local maxima for this function.To find the local maximum and minimum for ( f(x) = x^2 + 8x  12 ), follow these steps:
 Compute the derivative of the function: ( f'(x) = 2x + 8 ).
 Set the derivative equal to zero to find critical points: ( 2x + 8 = 0 ).
 Solve for ( x ) to find the critical point: ( x = 4 ).
 Determine the nature of the critical point by evaluating the second derivative: ( f''(x) = 2 ).
 Since the second derivative is positive ( ( f''(x) > 0 )), the critical point at ( x = 4 ) corresponds to a local minimum.
Therefore, the function ( f(x) = x^2 + 8x  12 ) has a local minimum at ( x = 4 ), and there is no local maximum.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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 What are the extrema of #f(x)=x^2192x+8 # on #x in[4,9]#?
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