Answer:
Average Rate of change of given function [tex]h(x)=-x^2-6x+17[/tex] is 2
Step-by-step explanation:
We are given function: [tex]h(x)=-x^2-6x+17[/tex] (considering x is missed)
We need to find average rate of change of the function over the interval [tex]- 6 < x < -2[/tex].
[tex]x_{1} = -6\\x_2 =-2[/tex]
Formula used to find average rate of change is: [tex]Average \ Rate \ of \ Change =\frac{h(x_2)-h(x_1)}{x_2-x1}[/tex]
Finding f(x₁) and f(x₂)
[tex]We \ have \ x_1=-6\\h(x_1)= -x^2-6x+17\\h(x_1)=-(-6)^2-6(-6)+17\\h(x_1)=-36+36+17\\h(x_1)=17[/tex]
[tex]We \ have \ x_2=-2\\h(x_2)=-x^2-6x+17\\h(x_2)=-(-2)^2-6(-2)+17\\h(x_2)=-4+12+17\\h(x_2)=25[/tex]
Putting values in the formula of average rate of change
[tex]Average \ Rate \ of \ Change =\frac{h(x_2)-h(x_1)}{x_2-x1}\\h(x_2)=25, h(x_1)=17, x_1 =-6 \ and \ x_2=-2\\Average \ Rate \ of \ Change =\frac{25-17}{-2-(-6)}\\Average \ Rate \ of \ Change =\frac{8}{4}\\Average \ Rate \ of \ Change =2[/tex]
So, Average Rate of change of given function [tex]h(x)=-x^2-6x+17[/tex] is 2
