(Solved): The limit represents the derivative of some function \( f \) at some number \( a . \) State such a ...

The limit represents the derivative of some function \( f \) at some number \( a . \) State such an \( f \) and \( a \). \[ \begin{aligned} \lim _{x \rightarrow 3} \frac{x^{4}-81}{x-3} \\ f(x)=x^{4}, & a=3 \\ f(x)=x^{4}, & a=81 \\ f(x)=x^{4}, & a=4 \\ f(x)=x^{5}, & a=27 \\ f(x)=\sqrt[4]{x}, & a=81 \end{aligned} \]