Question

Question #d7d5a

Answer 1

`a=3` and `f(x)=x^4`

Explanation:

The definition of the derivative of `y=f(x)` is

`f'(x)=lim_(h rarr 0) ( f(x+h)-f(x) ) / h`

Compare this derivative definition with the given limit:

`f'(a) = lim_(h rarr 0) ( (3+h)^4-81 ) / h = lim_(h rarr 0) ( (3+h)^4-3^4 ) / h`

And we see that `a=3` and that `f(x)=x^4`