Suppose is continuous on the closed interval and its average value on that interval is

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

Problem

Suppose

f

is continuous on the closed interval

[1,5]

and its average value on that interval is

3.2

. Explain why there must exist a number

c

(1,5)

such that

f(c)=3.2

, and identify the theorem that guarantees this fact.