Answer
(a) $17$
(b) $-1$
(c) $11$
Work Step by Step
Given $g(x)=x^3-2x+1$, we have the average rate of change $R=\dfrac{g(x_2)-g(x_1)}{x_2-x_1}$
(a) From $x_1=-3$ to $x_2=-2$, we have
$R=\dfrac{g(-2)-g(-3)}{-2-(-3)}=\dfrac{(-2)^3-2(-2)+1-[(-2)^3-2(-2)+1]}{1}=17$
(b) From $x_1=-1$ to $x_2=1$, we have
$R=\dfrac{g(1)-g(-1)}{1-(-1)}=\dfrac{(1)^3-2(1)+1-[(-1)^3-2(-1)+1]}{2}=-1$
(c) From $x_1=1$ to $x_2=3$, we have
$R=\dfrac{g(3)-g(1)}{3-1}=\dfrac{(3)^3-2(3)+1-[(1)^3-2(1)+1]}{2}=11$
