Let $f(x)=\sin x^2, \: x \in \mathbb{R}$. Then
- $f$ has no local minima
- $f$ has no local maxima
- $f$ has local minima at $x=0$ and $x=\pm\sqrt{(k+\frac{1}{2} ) \pi}$ for odd integers $k$ and local maxima at $x=\pm\sqrt{(k+\frac{1}{2} ) \pi}$ for even integers $k$
- None of the above