Mathematics

Mathematics

Problem

A continuous function

r

satisfies the following. •

r(x)>0

on

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

on

2<x<5

and the region between the graph of

r

and the

x

-axis over that interval has area

4

. •

r(x)>0

on

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

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