Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local
minima. If necessary, round answers to two decimal places.
-$$f ( x ) = x ^ { 3 } - 12 x + 2 ; ( - 5,5 )$$
A) local maximum at $( - 2,18 )$
local minimum at $( 0,0 )$
local minimum at $( 2 , - 14 )$

B) local minimum at $( 0,0 )$

C) local maximum at $( - 2,18 )$
local minimum at $( 2 , - 14 )$

D) none

Question

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local
minima. If necessary, round answers to two decimal places.
-$$f ( x ) = x ^ { 3 } - 12 x + 2 ; ( - 5,5 )$$
A) local maximum at $( - 2,18 )$
local minimum at $( 0,0 )$
local minimum at $( 2 , - 14 )$

B) local minimum at $( 0,0 )$

C) local maximum at $( - 2,18 )$
local minimum at $( 2 , - 14 )$

D) none

Quizplus · Accepted Answer

To find the local maxima and minima, we first find the derivative of the function $f(x) = x^3 - 12x + 2$, which is $f'(x) = 3x^2 - 12$. Setting the derivative equal to zero gives the critical points: $3x^2 - 12 = 0 \Rightarrow x^2 = 4 \Rightarrow x = \pm 2$. Evaluating the function at these points gives $f(-2) = (-2)^3 - 12(-2) + 2 = 18$ and $f(2) = (2)^3 - 12(2) + 2 = -14$. Thus, there is a local maximum at $(-2, 18)$ and a local minimum at $(2, -14)$, matching option C.

Use a Graphing Utility to Graph the Function Over the Indicated