Let $f(x)=\operatorname{Max}\{\cos x, \sin x, 0\}$. If the number of points at which $f(x)$ is not differentiable in $(0,2024 \pi)$ is $1012 k$, then $\mathrm{k}=$

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Aicharya · Accepted Answer

$\because f(x)=\max \{\cos x, \sin x, 0\}$

The bold curve in the above figure is the graph of $f(x)$. From figure, it is clear that $f(x)$ is periodic. $f(x)$ has 3 sharp edge between 0 to $2 \pi$. $\therefore f(x)$ is not differentiable at 3 points between 0 to $2 \pi$. i.e. $2 \pi \rightarrow 3$ $2024 \pi \rightarrow 3 \times 1012$ No. of points at which $f(x)$ is differentiable in $(0,2024 \pi)$ $=3 \times 1024$ $\Rightarrow 1012 k=3 \times 1024 \Rightarrow k=3$.

Let $f(x)=\operatorname{Max}\{\cos x, \sin x, 0\}$. If the number of points at which $f(x)$ is not…

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