Question

Given the function h(x)=-x^2+4x+12, determine the average rate of change of the function over the interval −2≤x≤4.

Answer 1

2

Explanation:

The average rate of change of h(x) in the closed interval [ a, b ] is

`(f(b) - f(a))/(b-a)`

Here [ a, b ] = [ - 2, 4 ] , then

f(b) = f(4) = - (4)² + 4(4) + 12 = - 16 + 16 + 12 = 12

f(a) = f(- 2) = - (- 2)² + 4(- 2) + 12 = - 4 - 8 + 12 = 0

Then

average rate of change =
`(12-0)/(4-(-2))` =
`(12)/(6)` = 2