Answer
$ f(x)=x^{-1}$ and $ a=\frac{1}{4}$
Work Step by Step
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}$
