Question

Given the function h(x)=-x^2 + X+4 determine the average rate of change of function over interval -1< x < 5

Answer 1

- 3

Explanation:

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

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

Here [ a, b ] = [ - 1, 5 ] , then

h(b) = h(5) = - 5² + 5 + 4 = - 25 + 9 = - 16

h(a) = h(- 1) = - (- 1)² + (- 1) + 4 = - 1 - 1 + 4 = 2

average rate of change =
`(-16-2)/(5-(-1))` =
`(-18)/(6)` = - 3