Answer
(a). $17$,
(b). $-1$,
(c). $11$.
Work Step by Step
(a). From $x_1=-3$ to $x_2=-2$, we have the average rate of change as $\frac{g(x_2)-g(x_1)}{x_2-x_1}=\frac{((-2)^3-2(-2)+1)-((-3)^3-2(-3)+1)}{-2+3}=17$,
(b). From $x_1=-1$ to $x_2=1$, we have the average rate of change as $\frac{g(x_2)-g(x_1)}{x_2-x_1}=\frac{((1)^3-2(1)+1)-((-1)^3-2(-1)+1)}{1+1}=-1$,
(c). From $x_1=1$ to $x_2=3$, we have the average rate of change as $\frac{g(x_2)-g(x_1)}{x_2-x_1}=\frac{((3)^3-2(3)+1)-((1)^3-2(1)+1)}{3-1}=11$.
