How do you find the coordinates of relative extrema #f(x)=x^34x^2+x+6#?
Setting the derivative to zero, and solving the equation will give you the
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To find the coordinates of relative extrema for the function ( f(x) = x^3  4x^2 + x + 6 ), follow these steps:
 Find the first derivative of the function ( f'(x) ).
 Set ( f'(x) ) equal to zero and solve for ( x ) to find critical points.
 Use the second derivative test or examine the behavior of ( f'(x) ) around critical points to determine whether each critical point corresponds to a relative minimum, relative maximum, or neither.
 For each relative extremum, substitute the ( x )coordinate into the original function to find the corresponding ( y )coordinate.
Let's go through each step:

Find the first derivative: [ f'(x) = 3x^2  8x + 1 ]

Set ( f'(x) ) equal to zero and solve for ( x ) to find critical points: [ 3x^2  8x + 1 = 0 ] This is a quadratic equation. You can solve it using the quadratic formula or factoring.

Solve for ( x ) to find critical points.

Use the second derivative test or analyze the behavior of ( f'(x) ) to determine the nature of each critical point.

Once you have identified the critical points, substitute each critical point's ( x )coordinate into the original function to find the corresponding ( y )coordinate.
This process will give you the coordinates of the relative extrema for the function ( f(x) = x^3  4x^2 + x + 6 ).
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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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