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:

Average rate of change $=-2$

Step-by-step explanation:

First derivative of function represents rate of change.

$\frac{d}{dx}hx=\frac{d}{dx}(-x^2+8x+24)\\\\=-2x+8$

Now find out rate of change at end points

$(\frac{dh}{dx})_{x=0}=-2\times 0+8=8\\\\\\(\frac{dh}{dx})_{x=9}=-2\times 9+8=-10$

average rate of changes =$\frac{First\ derivative\ at\ last\ point\ -first\ derivative\ at\ initial\ point }{last\ point-initial\ point}$

$=\frac{-10-8}{9-0}\\\\=\frac{-18}{9}\\\\=-2$