A function is continuous on with

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A function

f

is continuous on

[0,8]

with

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

. Suppose

g(8)=20

and

f(4)=3

. Decide whether the average value of

f

[0,8]

is greater than, equal to, or less than

f(4)

, and support your conclusion with a numerical argument.