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  • Which of the following functions is not differentiable at  <img alt="\mathrm{x=0 \text {. }}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%3D0%20%5Ctext%20%7B.%20%7D%7D"

Which of the following functions is not differentiable at  \mathrm{x=0 \text {. }}

Option: 1

\mathrm{|\sin x|}


Option: 2

\mathrm{|\cos x|}


Option: 3

\mathrm{|\sin x+\cos x|}


Option: 4

\mathrm{|\sin x-\cos x|}


Answers (1)

best_answer

Since cos x and \mathrm{\sin x+\cos x} are positive in a neighborhood of \mathrm{x=0} so their modules are differentiable similarly \mathrm{\sin x-\cos x} is negative and so their modules are differentiable but \mathrm{\sin \mathrm{x}} changes sign in the neighbourhood of \mathrm{\mathrm{x}= 0 .}

Posted by

Ritika Kankaria

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