Answer
$-3$
Work Step by Step
The general formula for the average rate of change from $x$ to $y$ can be written as: $\dfrac{f(y)-f(x)}{y-x}$. As $y\rightarrow x$, the rate of change becomes instantaneous (derivative).
Here, we have: $f(x)=x^2-3x$
$\lim\limits_{x\to 0}\dfrac{f(x)-f(0)}{x-0}=\lim\limits_{x\to 0}\dfrac{(x^2-3x)-[(0)^2-(3)(0)]}{x} \\=\lim\limits_{x\to 0}\dfrac{x(x-3)}{x} \\=\lim\limits_{x\to 0} (x-3) \\=0-3 \\=-3$
