A continuous function has average value on

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A continuous function

f

has average value

7

[0,2]

. Define

g(x)=5f(4x)+D

and consider

g

on the interval

[0,\tfrac12]

. (i) Express the average value of

g

[0,\tfrac12]

in terms of

D

. (ii) Determine the value of

D

for which the average value of

g

[0,\tfrac12]

20