Answer
(a) $2x-2$
(b) $-4$, $0$, $2$
Work Step by Step
(a) $f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}=\lim_{h\to0}\frac{(x+h)^2-2(x+h)-(x^2-2x)}{h}=\lim_{h\to0}\frac{2xh+h^2-2h}{h}=\lim_{h\to0}(2x+h-2)=2x-2$
(b) $f'(-1)=2(-1)-2=-4$, $f'(1)=2(1)-2=0$, $f'(2)=2(2)-2=2$
