A continuous function satisfies the following

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

A continuous function

r

satisfies the following. •

r(x)>0

0<x<2

and the region bounded by the graph of

r

and the

x

-axis over that interval has area

6

. •

r(x)<0

2<x<5

and the region between the graph of

r

and the

x

-axis over that interval has area

4

. •

r(x)>0

5<x<6

and the region bounded by the graph of

r

and the

x

-axis over that interval has area

3

. Define

R(x)=\displaystyle\int_{0}^{x} r(t)\,dt

for

0\le x\le 6

. At which of the following

x

-values does

R

attain its absolute maximum on

[0,6]

? (a)

x=6

(b)

x=5

(c)

x=2

(d)

x=0