Limit Continuity and Differentiability 7 Question 22
22. The function $f(x)=\left(x^{2}-1\right)\left|x^{2}-3 x+2\right|+\cos (|x|)$ is not differentiable at
$(1999,2 M)$
(a) -1
(b) 0
(c) 1
(d) 2
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Answer:
Correct Answer: 22. $(b, c, d)$
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 all $R-{0}$.
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 $x \in R-{0}$.
