Question

The function y=f(x) is graphed below. What is the average rate of change of the function f(x) on the interval −4≤x≤−2?

Answer 1

Okay, here we have this:

Considering the provided graph of the function and interval, we are going to calculate the requested average rate of change, so we obtain the following:

So to calculate the average rate of change, we will use the following formula:

`A(\lbrack a,b\rbrack)=(f(b)-f(a))/(b-a)`

Replacing:

`\begin{gathered} A(\lbrack-4,-2\rbrack)=(f(-2)-f(-4))/(-2-(-4)) \\ =(-8-(-2))/(-2-(-4)) \\ =(-8+2)/(-2+4) \\ =(-6)/(2) \\ =-3 \end{gathered}`

Finally we obtain that the average rate of change of the function f(x) on the interval −4≤x≤−2 is -3.