Let $f:R\rightarrow R$ be such that $f(1)=3$ and $f'(1)=6$. Then $\lim\limits_{x\to 0}\big[\large\frac{f(1+x)}{f(1)}\big]^{\Large\frac{1}{x}}$ equals

Question

$(a)\;1\qquad(b)\;e^{\Large\frac{1}{2}}\qquad(c)\;e^2\qquad(d)\;e^3$