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Question

Find whether the function is differentiable at x = 1 and x = 2
fx=xx12-x-2+3x-x21x2x>2

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Solution

fx=xx12-x-2+3x-x21x2x>2f'x=1x1-13-2x1x2x>2
Now,LHL=limx1- f'x=limx1- 1=1RHL=limx1+ f'x=limx1+ -1=-1Since, at x=1, LHLRHLHence, fx is not differentiable at x=1Again,LHL=limx2- f'x=limx2- -1=-1RHL=limx2+ f'x=limx2+ 3-2x=3-4=-1Since, at x=2, LHL=RHLHence, fx is differentiable at x=2

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