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:

  1. 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 $x \in R-{0}$.



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