Given continuous functions and on such that for for

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Given continuous functions

f

and

g

[0,4]

such that

f(x)>g(x)

for

0\le x<2

f(2)=g(2)

, and

g(x)>f(x)

for

2<x\le 4

. Suppose the area between the graphs of

f

and

g

from

x=0

x=2

equals the area between the graphs from

x=2

x=4

. Which statement correctly compares the average values of

f

and

g

[0,4]

? (a) The average value of

g

[0,4]

is greater than that of

f

. (b) There is not enough information to determine which average is greater. (c) The average values of

f

and

g

[0,4]

are equal. (d) The average value of

f

[0,4]

is greater than that of

g