#### Answer

$f(x)=x^6$ and $a=2$

#### 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
$$f'(a)=\lim\limits_{x\to 2}\frac{x^6-64}{x-2}$$
$$f'(a)=\lim\limits_{x\to 2}\frac{x^6-2^6}{x-2}$$
Now we match the formula found above with the formula of the derivative according to (1).
We find that $a=2$, $f(a)=f(2)=2^6$ and $f(x)=x^6$