Answer
(a) $-\frac{2h}{a(a+h)}$
(b) $-\frac{2}{a(a+h)}$
Work Step by Step
We are given: $f(t)=\frac{2}{t}$; $t=a$, $t=a+h$
(a) We calculate the net change:
$f(a+h)-f(a)=\displaystyle \frac{2}{a+h}-\frac{2}{a}=\frac{2a}{(a+h)a}-\frac{2(a+h)}{a(a+h)}=-\frac{2h}{a(a+h)}$
(b) We calculate the average rate of change:
$\displaystyle \frac{f(a+h)-f(a)}{(a+h)-a}=\frac{-\frac{2h}{a(a+h)}}{h}=-\frac{2h}{ah(a+h)}=-\frac{2}{a(a+h)}$
