Question

Given the function h(x)=-x^2+8x+24, determine the average rate of change of the function over the interval 0 is less than or equal to x is less than or equal to 9

Answer 1

Answer: ordered pairs (-2,-5) and (6,35)

Explanation:

Answer 2

Average rate of change
`=-2`

Explanation:

First derivative of function represents rate of change.

`(d)/(dx)hx=(d)/(dx)(-x^2+8x+24)\\\\=-2x+8\\`

Now find out rate of change at end points

`((dh)/(dx))_(x=0)=-2* 0+8=8\\\\\\((dh)/(dx))_(x=9)=-2* 9+8=-10`

average rate of changes =
`(First\ derivative\ at\ last\ point\ -first\ derivative\ at\ initial\ point )/(last\ point-initial\ point)`

`=(-10-8)/(9-0)\\\\=(-18)/(9)\\\\=-2`