Answer
See below
Work Step by Step
$\lim\limits_{x \to a} \frac{f(x)-f(a)}{x-a}$ or $\lim\limits_{h \to 0} \frac{f(h+a)-f(a)}{h}$ is $f'(a)$
The derivative f' is the instantaneous rate of change with respect to x when $x=a$ and also the slope of the tangent line at a.