What are the local extrema, if any, of #f (x) = x^312x+2 #?
The function has 2 extrema:
To find extrema we calculate derivative
Now we have to check if the derivative changes sign at the calcolated points:
graph{x^24 [10, 10, 4.96, 13.06]}
By signing up, you agree to our Terms of Service and Privacy Policy
To find the local extrema of ( f(x) = x^3  12x + 2 ), we first need to find the critical points by setting the derivative equal to zero and solving for ( x ). Then we can determine if these critical points correspond to local maxima or minima.

Find the derivative of ( f(x) ): [ f'(x) = 3x^2  12 ]

Set ( f'(x) ) equal to zero and solve for ( x ): [ 3x^2  12 = 0 ] [ x^2  4 = 0 ] [ x = \pm 2 ]

Determine the nature of the critical points:
 To the left of ( x = 2 ), ( f'(x) ) changes from negative to positive, indicating a local minimum.
 To the right of ( x = 2 ), ( f'(x) ) changes from positive to negative, indicating a local maximum.
 To the left of ( x = 2 ), ( f'(x) ) changes from negative to positive, indicating a local minimum.
 To the right of ( x = 2 ), ( f'(x) ) changes from positive to negative, indicating a local maximum.
Therefore, the local extrema of ( f(x) ) are:
 Local minimum at ( x = 2 )
 Local maximum at ( x = 2 )
By signing up, you agree to our Terms of Service and Privacy Policy
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.
 What are the local extrema, if any, of #f (x) = x^312x+2 #?
 How many local extrema can a cubic function have?
 How do you find the critical numbers of #f(x)=x^26x#?
 How to find the max and minimum of #f(x)= abs(x1 )+ 2abs(x+5) + 3abs(x4)# using derivatives?
 How do you find the critical numbers of #f(x)=x^(2/3)+x^(1/3)#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7