AP

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

Problem

Let

f(x)=x^{2}+2x+1

for

-1\le x\le 3

. (a) Calculate the average value of

f

on the interval

[-1,3]

. (b) Determine all value(s) of

c

[-1,3]

for which

f(c)

equals the average value found in part (a). Show algebraic work leading to each solution.