Let $f(x)=e^{x^2}.$ It can be shown by direct computation that $f^{(4)}(x) \le 76 e$ on the interval [0, 1]. Using this information and the appropriate error formula, how large should $n$ be so that the Simpson's Rule approximation to $\int_{0}^{\,1} {e^{x^2}}\, dx$ is accurate to within 0.00001? (Your answer must be a whole number.)

$n =$