The graph of

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

Problem

The graph of

g'

, the derivative of a differentiable function

g

, is composed of straight‐line segments with the following characteristics. • For

x<0

g'(x)=0

. • On

0\le x\le 2

g'(x)=2

. • On

2\le x\le5

g'(x)

decreases linearly from

2

x=2

-4

x=5

. • For

x\ge5

g'(x)=-4

. Assume

g(0)=3

. (a) Compute

g(2)

g(5)

, and

g(7)

. Show all steps in your reasoning. (b) On the interval

0\le x\le7

, determine the

x

–value at which

g

attains its absolute maximum. Justify your answer using information from the graph of

g'