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Question

If f(x)={x,for x00,for x>0
then f(x) at x=0 is

A
Continuous but not differentiable
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B
Not continuous but differentiable
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C
Continuous and differentiable
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D
Not continuous and not differentiable
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Solution

The correct option is A Continuous but not differentiable
Continuity at x=0
limx0f(x)=limx0x=0
limx0+f(x)=0
f(0)=0
continuous at x=0
For differentiablility
f(x)={1, x00, x>0
not differentiable
It has sharp edge at x=0
not differentiable but continuous.
679532_639431_ans_f4e716a943b64b5da88b8c250e8e6370.png

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