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Question

If f(x)=min{x2,x+1,sgn|x|} then f(x) is
(where sgn(x) denotes signum function of x)

A
continuous at x=0
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B
discontinuous at one point
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C
non-differentiable at 3 points
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D
differentiable at x=12
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Solution

The correct option is D differentiable at x=12
By the figure given above we can say that f(x) graph will be

The curves x2 and x+1 intersect at x2=x+1 x2+x1=0
x=1±52
f(x) is continuous for all real numbers but not differentiable at x=1,1+52
So, f(x) is continous at x=0 and differentiable at x=12.

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