Question

Given the function h(x) = —~2 – 6x + 17, determine the average rate of change

Answer 1

Answer:

Average Rate of change of given function $h(x)=-x^2-6x+17$ is 2

Step-by-step explanation:

We are given function: $h(x)=-x^2-6x+17$ (considering x is missed)

We need to find average rate of change  of the function over the interval $- 6 < x < -2$.

$x_{1} = -6\\x_2 =-2$

Formula used to find average rate of change is: $Average \ Rate \ of \ Change =\frac{h(x_2)-h(x_1)}{x_2-x1}$

Finding f(x₁) and f(x₂)

$We \ have \ x_1=-6\\h(x_1)= -x^2-6x+17\\h(x_1)=-(-6)^2-6(-6)+17\\h(x_1)=-36+36+17\\h(x_1)=17$

$We \ have \ x_2=-2\\h(x_2)=-x^2-6x+17\\h(x_2)=-(-2)^2-6(-2)+17\\h(x_2)=-4+12+17\\h(x_2)=25$

Putting values in the formula of average rate of change

$Average \ Rate \ of \ Change =\frac{h(x_2)-h(x_1)}{x_2-x1}\\h(x_2)=25, h(x_1)=17, x_1 =-6 \ and \ x_2=-2\\Average \ Rate \ of \ Change =\frac{25-17}{-2-(-6)}\\Average \ Rate \ of \ Change =\frac{8}{4}\\Average \ Rate \ of \ Change =2$

So, Average Rate of change of given function $h(x)=-x^2-6x+17$ is 2