Question

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 2 << 8. 2 82 4 52 6 30 8 16 10 12 12

Answer 1

The average rate of change of a function is determined by

$\frac{f(b)-f(a)}{b-a}$

using the interval that you were given select the two corresponding points in the table ( 2 & 8 )

Point a (2,82)

Point b (8,16)

Replace the points into the formula

$\begin{gathered} \frac{16-82}{8-2} \\ \frac{-66}{6} \\ -11 \end{gathered}$

The average rate of change of the function over the inverval [2,8] will be -11