Question

You don’t have to do all of them. Just do any one of them so I could figure out the steps to solve it. Thanks!(a) = [-3, -1]

Answer 1

We are given the following function

`f(x)=2x^2-12`

We are asked to find the average rate of change for the above function in the interval [-3, -1]

The average rate of change for a function is given by

`A(x)=(f(b)-f(a))/(b-a)`

For the given case, the interval is [a, b] = [-3, -1]

This means that a = -3 and b = -1

Let us evalute the function at a = -3 and b = -1

`\begin{gathered} f(-3)=2(-3)^2-12=2(9)-12=18-12=6 \\ f(-1)=2(-1)^2-12=2(1)-12=2-12=-10 \end{gathered}`

So, we have

f(-3) = f(a) = 6

f(-1) = f(b) = -10

`A(x)=(f(b)-f(a))/(b-a)=(-10-6)/(-1-(-3))=(-16)/(-1+3)=(-16)/(2)=-8`

Therefore, the average rate of change for the function is -8 in the interval [-3, -1]