Question

Given the function defined in the table below, find the average rate of change, in

simplest form, of the function over the interval 1 < x < 5.
2
f(x)
1
77
2
68
3
59
4
50
5
5
41
-

Answer 1

Given:

Function interval

`1\leq x\leq5`
`\begin{gathered} x\rightarrow f(x) \\ \\ 1\rightarrow77 \\ \\ 2\rightarrow68 \\ \\ 3\rightarrow59 \\ \\ 4\rightarrow50 \\ \\ 5\rightarrow41 \end{gathered}`

Find-: Average rate of change.

Sol:

The average rate of change is:

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

Choose any two-point.

`\begin{gathered} (x_1,y_1)=(1,77) \\ \\ (x_2,y_2)=(2,68) \end{gathered}`

So average rate of change is:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \\ m=(68-77)/(2-1) \\ \\ m=(-9)/(1) \\ \\ m=-9 \end{gathered}`

The average rate of change is -9.