If $f(x) = x(\sqrt{x} - \sqrt{x + 1}),$ then

Let $f : R \to R$ be differentiable at $c \in R$ and $f(c) = 0$. If $g(x) = |f(x)|$,then at $x = c$,$g$ is

The function given by $y = ||x| - 1|$ is differentiable for all real numbers except the points

Let $f: R \rightarrow R$ and $g: R \rightarrow R$ be respectively given by $f(x)=|x|+1$ and $g(x)=x^2+1$. Define $h: R \rightarrow R$ by $h(x)=\begin{cases} \max \{f(x), g(x)\} & \text{if } x \leq 0 \\ \min \{f(x), g(x)\} & \text{if } x > 0 \end{cases}$. The number of points at which $h(x)$ is not differentiable is

Let $f:R \to R$ be a function defined by $f(x) = \text{Min}\{x + 1, |x| + 1\}$. Then which of the following is true?

Define a function $f: R \rightarrow R$ by $f(x) = \begin{cases} \frac{\sin x^2}{x}, & \text{for } x < 0 \\ x^2 + ax + b, & \text{for } x \geq 0 \end{cases}$. Suppose $f(x)$ is differentiable on $R$. Then,