Answer
(a) $2a-3$
(b) $1$, $-7$
Work Step by Step
(a) $$f'(a)=\lim_{h\to0}\frac{f(a+h)-f(a)}{h}=\lim_{h\to0}\frac{(a+h)^2-3(a+h)-(a^2-3a)}{h}=\lim_{h\to0}\frac{(2ah+h^2-3h)}{h}=\lim_{h\to0}(2a+h-3)=2a-3$$
(b) $f'(2)=2\times2-3=1$ and $f'(-2)=-2\times2-3=-7$
