Answer
a.)$\frac{-2}{\pi}$
b.) 0
Work Step by Step
The definition of average rate of change is
$\frac{f(x2) - f(x1)}{x2-x1}$.
a.) g(t) = 2 + cos t
interval = [0, $\pi$]
$\frac{g(\pi) - g(0)}{\pi - 0}$.
g($\pi$) = 2 + cos $\pi$ = 2-1 = 1
g(0) = 2 + cos(0) = 2 + 1 = 3
$\frac{1 -3}{\pi - 0}$. = $\frac{-2}{\pi}$
b.) g(t) = 2 + cos t
interval = [-$\pi$, $\pi$]
$\frac{g(\pi) - g(-\pi)}{\pi - (-\pi)}$.
g($\pi$) = 2 + cos $\pi$ = 2-1 = 1
g(-$\pi$) = 2 + cos(-$\pi$) = 2 - 1 = 1
$\frac{1 -1}{\pi - (-\pi)}$. = $\frac{0}{2\pi}$
=0
