Question

At what value c does the function f(x) = 2x - 8 take on the average value f(c) over the interval (2,8) ?

Answer 1

c = 5.

Explanation:

f(2) = 2(2) - 8 = -4

f(8) = 2(8) - 8 = 8

The mean of f(x) over the interval is when (-4+8)/2 = 2.

So 2c - 8 = 2

2c = 10

c = 5.