The total number of points of non-differentiability of $f(x) = \min \{ |\sin x|, |\cos x|, \frac{1}{4} \}$ in $(0, 2\pi)$ is

Let $f(x) = 15 - |x - 10|; x \in R$. Then the set of all values of $x$,at which the function $g(x) = f(f(x))$ is not differentiable,is

Let $f(x) = \begin{cases} a \cot^{-1} \left( \frac{b+x}{4} \right), & \frac{-2}{3} < x < 0 \\ 2, & x = 0 \\ \frac{\ln(1-cx)}{x}, & 0 < x < \frac{2}{3} \end{cases}$. If the function $f(x)$ is differentiable at $x = 0$,then find the value of $(b^2 - 2a + c^6)$.

If $f(x) = |x|,$ then $f'(0) = $

If both $f(x)$ and $g(x)$ are differentiable functions at $x = x_0$,then the function defined as $h(x) = \text{Maximum} \{f(x), g(x)\}$:

Consider the function $f:(0, \infty) \rightarrow \mathbb{R}$ defined by $f(x)=e^{-\left|\log _e x\right|}$. If $m$ and $n$ are respectively the number of points at which $f$ is not continuous and $f$ is not differentiable,then $m+n$ is