Limit Continuity And Differentiability Ques 119

Answer:

Correct Answer: 119.$(b, c, d)$

Solution:

119. Given, $f(x)=x|x|$

$$ \Rightarrow \quad f(x)=\begin{array}{ll} x^{2}, & \text{if } x \geq 0 \\ -x^{2}, & \text { if } x<0 \end{array} $$

$f(x)$ is not differentiable at $x=0$ but is differentiable for all $x \in \mathbb{R} \setminus {0}$.

Therefore, $\quad f^{\prime}(x)=\begin{array}{ll}2 x, & x>0 \ -2 x, & x<0\end{array}$

Therefore, $f(x)$ is twice differentiable for all $x \in \mathbb{R}-{0}$.