Answer
f'(x)= -2x
f'(-3) = 6
f'(0) = 0
f'(1) = -2
Work Step by Step
f(x) = $4-x^{2}$
f'(x) = $\lim\limits_{h \to 0}\frac{f(x+h)-f(x)}{h}$
=$\lim\limits_{h \to 0}\frac{[4-(x+h)^{2}]-(4-x^{2})}{h}$
=$\lim\limits_{h \to 0}\frac{4-x^{2}-h^{2}-2xh-4+x^{2}}{h}$
= $\lim\limits_{h \to 0}-h-2x$= -0-2x = -2x
f'(-3) = -2×(-3)= 6
f'(0) = -2×0 = 0
f'(1) = -2×1 = -2
