## Calculus (3rd Edition)

$f(x)=x^{-1}$ and $a=\frac{1}{4}$
The derivative $f'(a)$ is defined as $f'(a)=\lim\limits_{x \to a}\frac{f(x)-f(a)}{x-a}$ Comparing $\lim\limits_{x \to \frac{1}{4}}\frac{x^{-1}-4}{x-\frac{1}{4}}$ with the above definition, we get $a=\frac{1}{4}$ and $f(x)=x^{-1}$