Answer
$f(x)=\frac{1}{x}$ and $a=\frac{1}{4}$
Work Step by Step
*Another way to write the derivative of a function $f$ at a number $a$ is $$f'(a)=\lim\limits_{x\to a}\frac{f(x)-f(a)}{x-a}\hspace{0.5cm}(1)$$
Here we have
$$f'(a)=\lim\limits_{x\to 1/4}\frac{\frac{1}{x}-4}{x-\frac{1}{4}}$$
$$f'(a)=\lim\limits_{x\to 1/4}\frac{\frac{1}{x}-\frac{1}{1/4}}{x-1/4}$$
Now we match the formula found above with the formula of the derivative according to (1).
We find that $a=\frac{1}{4}$, $f(a)=f(\frac{1}{4})=\frac{1}{1/4}$ and $f(x)=\frac{1}{x}$
