Question

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3 < x < 6. х f(x) 0 8 3 10 6 12 9 14 12 16

Answer 1

in the interval

`3\le x\le6`

we can see that

`\begin{gathered} \text{when x=3, y=f(x)=10} \\ \text{when x=6, y=f(x)=12} \end{gathered}`

the average rate of change is the slope m. The formula for m is

`m=(y_2-y_1)/(x_2-x_1)`

where

`\begin{gathered} (x_1,y_1)=(3,10) \\ \text{and} \\ (x_2,y_2)=(6,12) \end{gathered}`

By substituying these values, we have

`m=(12-10)/(6-3)`

hence,

`m=(2)/(3)`

Therefore, the average rate of change is 2/3=0.667