Question

Help me out with this simple stuff please and thank you. Anyone. Show work.

Answer 1

The average rate of change of f on the interval [-4, -2] is -11.

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:

`\displaystyle f_\text{avg}(x) = (f(2)-f(-4))/(2-(-4))`

Evaluate:

`\displaystyle \begin{aligned} f_\text{avg}(x) & = (f(2)-f(-4))/(2-(-4)) \\ \\ & = ((-3)-(63))/(6) \\ \\ &= -11 \end{aligned}`

In conclusion, the average rate of change of f on the interval [-4, -2] is -11.