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Question

The number of points at which f(x)={min(x,x2),if <x<1min(2x1,x2),if x1 is not differentiable is

A
0
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B
1
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C
2
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D
3
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Solution

The correct option is B 1
f(x)={min(x,x2),if <x<1min(2x1,x2),if x1




f(x)=x,<x<0x2,0x<12x1,1x<f(x)=1,<x<02x,0x<12,1x<f(0)=1,f(0+)=0f(1)=2,f(1+)=2

As f(0)f(0+), so non differentiable at x=0
But f(1)=f(1+), so differentiable at x=1

Hence, f(x) is non differentiable at 1 point.

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