Answer
(a) $-\frac{4}{a^2}$
(b) $-1$, $-1$
Work Step by Step
(a) $$f'(a)=\lim_{h\to0}\frac{f(a+h)-f(a)}{h}=\lim_{h\to0}\frac{\frac{4}{a+h}-\frac{4}{a}}{h}=\lim_{h\to0}\frac{4a-4a-4h}{ah(a+h)}=\lim_{h\to0}\frac{-4}{a(a+h)}=-\frac{4}{a^2}$$
(b) $f'(2)=-\frac{4}{2^2}=-1$ and $f'(-2)=-\frac{4}{(-2)^2}=-1$
