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

$A(x)=\frac{f(b)-f(a)}{b-a}$

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

$A(x)=\frac{f(b)-f(a)}{b-a}=\frac{-10-6}{-1-(-3)}=\frac{-16}{-1+3}=\frac{-16}{2}=-8$

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