Question

Find the average rate of change of f(x)=-x^2+2x+2 from x=2 to x=6. Simplify your answer as much as possible.

Answer 1

Answer:

- 6

Step-by-step explanation:

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

$\frac{f(b)-f(a)}{b-a}$

Here [ a, b ] = [ 2, 6 ] , then

f(b) = f(6) = - 6² + 2(6) + 2 = - 36 + 12 + 2 = - 22

f(a) = f(2) = - 2² + 2(2) + 2 = - 4 + 4 + 2 = 2 , then

average rate of change = $\frac{-22-2}{6-2}$ = $\frac{-24}{4}$ = - 6