Mathematics

Problem

Let

g(x)=x^{3}-3x^{2}+2

for all real

x

. Which of the following correctly classifies the relative extrema of

g

? a) Local minimum at

(0,2)

and local maximum at

(2,-2)

b) Local maximum at

(0,2)

and local minimum at

(2,-2)

c) Local maximum only at

(2,-2)

; no other relative extrema d)

g

has no relative extrema