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  •  The function <img alt="\mathrm{f(x)=\left(x^{2}-1\right)\left|x^{2}-3 x+2\right|+\cos |x|}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bf%28x%29%3D%5Cleft%28x%5E%7B2%7D-1

 The function \mathrm{f(x)=\left(x^{2}-1\right)\left|x^{2}-3 x+2\right|+\cos |x|} is not differentiable at

Option: 1

-1


Option: 2

0


Option: 3

1


Option: 4

2


Answers (1)

best_answer

\mathrm{f(x)=(x+1)(x-1)|x-1| x-2 \mid+\cos x},  because

\mathrm{\cos |x|=\left\{\begin{array}{ll}\cos x, & \text { if } x \geq 0 \\ \cos (-x), & \text { if } x<0\end{array}=\cos x\right.}.

Since \mathrm{h(x)=x|x|} is differentiable at \mathrm{x=0}, so \mathrm{(x-1)|x-1|} is differentiable at \mathrm{x=1}. Also \mathrm{f(x)}  is not differentiable at \mathrm{x=2}.

Posted by

Devendra Khairwa

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