AP

MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Define

g(x)=(x^{2}-4)^{3}-2(x^{3}-1)(x-2)

. (a) Find

g'(x)

and express your answer in fully expanded and simplified polynomial form. (b) Solve

g'(x)=0

for

x

in the interval

[-2,3]

. (c) Using a first-derivative sign analysis on

[-2,3]

, classify each critical point found in part (b) as the location of a relative maximum, relative minimum, or neither.