Question

The function y=f(x)y is graphed below. What is the average rate of change of the function f(x) on the interval −5≤x≤−4?

Answer 1

Given:

`\begin{gathered} y=f(x) \\ \\ -5\leq x\leq-4 \end{gathered}`

Find-: Average rate of change.

Sol:

The average rate of change of f(x) int the closed interval [a,b] is:

`(f(b)-f(a))/(b-a)`

Here,

`[a,b]=[-5,-4]`

`\begin{gathered} f(b)=f(-4)=-15 \\ \\ f(a)=f(-5)=-15 \end{gathered}`

So average rate of change is:

`\begin{gathered} =(f(b)-f(a))/(b-a) \\ \\ =(-15-(-15))/(-4-(-5)) \\ \\ =(-15+15)/(-4+5) \\ \\ =(0)/(1) \\ \\ =0 \end{gathered}`

Average rate of change in given interval is 0.