Answer
(a). $-4$,
(b). $-8$,
(c). $-10$.
Work Step by Step
(a). From $x_1=0$ to $x_2=2$, we have the average rate of change as $\frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{(-2(2)^2+4)-(-2(0)^2+4)}{2-0}=\frac{-8}{2}=-4$,
(b). From $x_1=1$ to $x_2=3$, we have the average rate of change as $\frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{(-2(3)^2+4)-(-2(1)^2+4)}{3-1}=\frac{-16}{2}=-8$,
(c). From $x_1=1$ to $x_2=4$, we have the average rate of change as $\frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{(-2(4)^2+4)-(-2(1)^2+4)}{4-1}=\frac{-30}{3}=-10$.
