Answer:
The average rate of change of f on the interval [-4, -2] is -11.
Step-by-step explanation:
Recall that the average rate of change of a function over an interval is simply the slope of the line connecting the two endpoints.
Therefore, the average rate of change of f on the interval [-4, 2] equals:
[tex]\displaystyle f_\text{avg}(x) = \frac{f(2)-f(-4)}{2-(-4)}[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} f_\text{avg}(x) & = \frac{f(2)-f(-4)}{2-(-4)} \\ \\ & = \frac{(-3)-(63)}{6} \\ \\ &= -11 \end{aligned}[/tex]
In conclusion, the average rate of change of f on the interval [-4, -2] is -11.
