Question

Given the function defined in the tablebelow, find the average rate of change, insimplest form, of the function over theinterval 2 < x < 6.

Answer 1

Average rate of change over an interval is defined as:

`(f(x_2)-f(x_1))/(x_2-x_1)`

The interval define is :

`2\leq x\leq6`

This implies that the average rate of change over the interval is:

`\begin{gathered} (f(x_6)-f(x_2))/(x_6-x_1)=\text{ }(19-13)/(6-2) \\ \\ \text{The average rate of change over the interval=}(6)/(4)=(3)/(2) \end{gathered}`

Hence, the average rate of change over the interval is;

`(3)/(2)`