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