Answer
(a). $-2$,
(b). $0$,
(c). $5$.
Work Step by Step
(a). From $x_1=-1$ to $x_2=1$, we have the average rate of change as $\frac{h(x_2)-h(x_1)}{x_2-x_1}=\frac{((1)^2-2(1)+3)-((-1)^2-2(-1)+3)}{1+1}=-2$,
(b). From $x_1=0$ to $x_2=2$, we have the average rate of change as $\frac{h(x_2)-h(x_1)}{x_2-x_1}=\frac{((2)^2-2(2)+3)-((0)^2-2(0)+3)}{2-0}=0$,
(c). From $x_1=2$ to $x_2=5$, we have the average rate of change as $\frac{h(x_2)-h(x_1)}{x_2-x_1}=\frac{((5)^2-2(5)+3)-((2)^2-2(2)+3)}{5-2}=5$.
