Question

Given the function h(a) = -x^2+ 7x + 14, determine the average rate of change

of the function over the interval 1 < x < 8.
Answer:
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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 ] = [1, 8 ], thus

f(b) = f(8) = - 8² + 7(8) + 14 = - 64 + 56 + 14 = 6

f(a) = f(1) = - 1² + 7(1) + 14 = - 1 + 7 + 14 = 20

average rate of change =
`(6-20)/(8-1)` =
`(-14)/(7)` = - 2