Consider the function on the closed interval

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Consider the function f(x)=x3−3x+2f(x)=x^{3}-3x+2 on the closed interval [−3,3][-3,3]. Which of the following correctly identifies every local extremum of ff in the interval and states whether it is an absolute extremum? (a) Local maximum at x=−1x=-1 (not absolute); local minimum at x=1x=1 (not absolute) (b) Local maximum at x=−1x=-1 (absolute); local minimum at x=1x=1 (absolute) (c) Local maximum at x=3x=3 (absolute); local minimum at x=−3x=-3 (absolute) (d) Local maximum at x=1x=1 (not absolute); local minimum at x=−1x=-1 (not absolute)

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