Limit Continuity And Differentiability Ques 119
- The function $f(x)=\left(x^{2}-1\right)\left|x^{2}-3 x+2\right|+\cos (|x|)$ is not differentiable at
$(1999,2 M)$
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Answer:
Correct Answer: 119.$(b, c, d)$
Solution:
- 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 $x \in \mathbb{R}-{0}$.
BETA
