Question #a364e

Feb 9, 2017

instantaneous rate of change $= 20.94$

Explanation:

To find the instantaneous rate of change of f(x) at 3 we first find the average rate of f(x) between x=3 and x=3.5 and the average rate of f(x) between x=2.5 and x=3. Then find the average of the two average rates to get our answer.

That is,
${r}_{a v g} = \frac{f \left(3.5\right) - f \left(3\right)}{3.5 - 3} = \frac{33.12 - 20.09}{0.5} = 26.06$

${r}_{a v g} = \frac{f \left(3\right) - f \left(2.5\right)}{3 - 2.5} = \frac{20.09 - 12.18}{0.5} = 15.82$

instantaneous rate of change =$\frac{26.06 + 15.82}{2} = 20.94$