Question

Given the function g(x)= x² + x - 3determine the average rate of change of the function over the interval -3 ≤ x ≤ 6.

Answer 1

To determine the average rate of change of a given function over a given interval, we need to evaluate it in each of the extremes. In the given case, x = -3 and x = 6

Evaluating it, we have the following:

`\begin{gathered} g(-3)=(-3)^3+-3-3 \\ g(-3)=9-6 \\ g(-3)=3 \\ \\ g(6)=6^2+6-3 \\ g(6)=36+3 \\ g(6)=39 \end{gathered}`

Now, to calculate the average rate of change, by using the following formula:

`m=(g(x_2)-g(x_1))/(x_2-x_1)`

substituting x2 = 6 and x1 = -3, we have the following:

`\begin{gathered} m=(g(6)-g(-3))/(6-(-3)) \\ m=(39-3)/(6+3) \\ m=(36)/(9) \\ \\ m=4 \end{gathered}`

From the solution developed above, we are able to conclude that the average rate of the given function over the interval -3 ≤ x ≤ 6 is equal to:

4