Solution
= Solution
The <product rule> and <chain rule> give
$$
f'(x)=10e^{3-x^2}(1-2x^2).
$$
The <exponential function> is strictly positive, so there are exactly \b[two] <stationary points>, at $\boxed{x=\pm1/\sqrt2}$. The <derivative> is negative outside these two values and positive between them. Thus the negative value is a strict <local minimum> and the positive value a strict <local maximum>.