Answer
$-3$
Work Step by Step
Factor each polynomial:
$$f'(0)\\=\lim_{x\to 0}\frac{f(x)-f(0)}{x-0}\\=\lim_{x\to 0}\frac{x^2-3x-((0)^2-3(0))}{x}\\=\lim_{x\to 0}\frac{x^2-3x}{x}\\=\lim_{x\to 0}\frac{x(x-3)}{x}.$$
Cancel the common factors: $$\lim_{x\to 0}x-3\\=0-3=-3$$