Question

Given the function h(x)=-x^2-5x+14 determine the average rate of change of the function over the interval -9

Answer 1

The average rate of change of the function over the interval is of 6.

Explanation:

Average rate of change:

The average rate of change of a function h(x) over an interval [a,b] is given by:

`A = (h(b)-h(a))/(b-a)`

In this question:

Over the interval [-9,-2], so
`a = -9, b = -2, b - a = -2 -(-9) = 7`

The function is:

`h(x) = -x^2 - 5x + 14`

`h(-9) = -9^2 -5(-9) + 14 = -81 + 45 + 14 = -22`

`h(-2) = -2^2 -5(-2) + 14 = -4 + 10 + 14 = 20`

Then

`A = (h(-2)-h(-9))/(7) = (20-(-22))/(7) = (42)/(7) = 6`

The average rate of change of the function over the interval is of 6.