Finding a function from only knowing its derivative at a point. This question on my last calc exam, I am told is very easy, but I do not understand how it is possible.

$ \lim_{h \to 0} \frac{\sqrt[3]{27+h}-3}{h}$ is the derivative of $f(x)$ at point $a$.
Find $f(x)$ and find $a$.

I recognize the definition of the derivative.
Therefore I know that $f(a + h) = \sqrt[3]{27+h}$ and $f(a) = 3$
Then I am stuck.
What is this question asking? How can we know the integral (the entire function $f(x)$) from the derivative at a single point?
In lieu of an explanation I will accept an algorithm which I can use to solve it.

You don't know the function $f$ from the single derivative $f'(a)$. You know it from the expression $f(a+h)=\sqrt[3]{27+h}$, which holds for all $h$, so that you can simply substitute $h=x-a$ on both sides. The answer that you get will be valid for any number $a$ that you choose, so the question is somewhat strangely formulated ($a$ can be anything, i.e., it isn't at all determined by the given data).
