## Calculus (3rd Edition)

$f(x)=x^{3}$ and $a=5$
The derivative at a point $a$ is defined as $f'(a)=\lim\limits_{x \to a}\frac{f(x)-f(a)}{x-a}$ But, given that $f'(a)=\lim\limits_{x \to 5}\frac{x^{3}-125}{x-5}\,\,\,\,$ Comparing right-hand sides of both the equations above, we obtain $a=5$ and $f(x)=x^{3}$