Question

Given the function f(x)=-x^2+6x+17 determine the average rate of change of the function over the interval −3≤x≤7.

Answer 1

Answer:

2

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 ] = [ - 3, 7 ] , then

f(b) = f(7 ) = - 7² + 6(7) + 17 = - 49 + 42 + 17 = 10

f(a) = f(- 3) = - (- 3)² + 6(- 3) + 17 = - 9 - 18 + 17 = - 10

average rate of change = $\frac{10-(-10)}{7-(-3)}$ = $\frac{10+10}{7+3}$ = $\frac{20}{10}$ = 2