Embibe Experts Solutions for Chapter: Continuity and Differentiability, Exercise 2: EXERCISE-2

Let $f\left(x\right)=\left\{\begin{array}{cc}2x+3;& -3\le x<-2\\ x+1;& -2\le x<0\\ x+2;& 0\le x\le 1\end{array}\right.$. At what points the function is/are not differentiable in the interval $\left[-3,1\right]$

If $f\left(x\right)=\cos \pi \left(\left|x\right|+\left[x\right]\right),$ then $f\left(x\right)$ is/are (where $\left[·\right]$ denotes greatest integer function)

If $f\left(x\right)=\left|x+1\right|\left(\left|x\right|+\left|x-1\right|\right)$ then at what points the function is /are not differentiable at in the interval $\left[-2,2\right]$

Let $h\left(x\right)=\min \left\{x,x^2\right\}$, for every real number of $x$, Then-

A differentiable function $f\left(x\right)$ is strictly increasing $\forall x$ in $R,$ Then

If $f\left(0\right)=f\left(1\right)=f\left(2\right)=0$ and function $f\left(x\right)$ is twice differentiable in $\left(0,2\right)$ and continuous in $\left[0,2\right]$. Then which of the following is/are definitely true?

Consider the function $f\left(x\right)=\left\{\begin{array}{l}x\sin \frac{\pi }{x}, \mathrm{for} x>0\\ 0, \mathrm{for} x=0\end{array}\right.$. Then the number of points in $(0, 1)$ where the derivative vanishes is:

Let $f\left(x\right)=8x^3-6x^2-2x+1$, then