Let S be the set of all points in (-,) at which the function f(x)= x, x is not differentia…

Question

Let $S$ be the set of all points in $(-\pi,\pi)$ at which the function $f(x)=\min\{\sin x,\cos x\}$ is not differentiable. Then $S$ is a subset of which of the following?

Accepted Answer

$\sin x=\cos x$ at $x=-\dfrac{3\pi}4,\dfrac\pi4$ within $(-\pi,\pi)$, where the min switches branches with different slopes. So $S=\left\{-\dfrac{3\pi}4,\dfrac\pi4\right\}\subseteq\left\{-\dfrac{3\pi}4,-\dfrac\pi4,\dfrac{3\pi}4,\dfrac\pi4\right\}$.

Solutions · 1