The derivative of a function g is given by g′(x)=(x−2)(x+1)2. Which of the following correctly classifies the critical points of g?
a) g has a local maximum at x=2 and no extremum at x=−1.
b) g has a local minimum at x=2 and a local maximum at x=−1.
c) g has a local minimum at x=2 and no extremum at x=−1.
d) g has no extremum at x=2 and a local minimum at x=−1.