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Let $f(x)=\sin x^2, \: x \in \mathbb{R}$. Then

  1. $f$ has no local minima
  2. $f$ has no local maxima
  3. $f$ 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 $k$
  4. None of the above
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