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:
[tex]\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}[/tex]Now, to calculate the average rate of change, by using the following formula:
[tex]m=\frac{g(x_2)-g(x_1)}{x_2-x_1}[/tex]substituting x2 = 6 and x1 = -3, we have the following:
[tex]\begin{gathered} m=\frac{g(6)-g(-3)}{6-(-3)} \\ m=\frac{39-3}{6+3} \\ m=\frac{36}{9} \\ \\ m=4 \end{gathered}[/tex]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
