The graph of a continuous function on consists of two simple geometric regions above…

MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The graph of a continuous function

f

0\le x\le 4

consists of two simple geometric regions above the

x

–axis, described as follows. • For

0\le x\le 2

f(x)=3

so that the graph is a rectangle of height

3

. • For

2\le x\le 4

, the graph of

f

is a straight line segment with endpoints

(2,3)

and

(4,0)

. Define the accumulation function

g(x)=\int_{0}^{x} f(t)\,dt

with

g(0)=0

. (a) Calculate

g(2)

. Show all steps. (b) Calculate

g(4)

. (c) Determine the value of

x

in the interval

0\le x\le 4

at which

g

attains its maximum value. Justify your answer using properties of

f

and

g

. State the maximum value of

g