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Question

Let f(x)={2+1x2, |x|12e(1x)2, |x|>1
The points where f(x) is not differentiable is/are :

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Solution

Given function is f(x)={2+1x2,|x|12e(1x)2,|x|>1
Now, to check the differentiability of function
f(x)=⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪4e(1x)2(x1),x(,1)x1x2,x(1,1)4e(1x)2(x1),x(1,)

Clearly, left hand derivative at x=1
f(1) is not defined.
Also, right hand derivative at x=1
f(1+) is not defined.
Thus, f(x) is not differentiable at x=1,1.

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