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Question

Consider the following functions :
1. f(x)=1xifx00ifx=0
2. f(x)={2x+5ifx>0x2+2x+5ifx0
Which of the above functions is/are derivable at x=0?

A
1 only
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B
2 only
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C
Both 1 and 2
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D
Neither 1 nor 2
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Solution

The correct option is B 2 only
Solution:
1. Consider, f(0)
=limh0f(0+h)f(0)h=limh01/h0h
=limh01h2= (not defined)
Hence, 1 is not differentiable at x=0
2. We have, f(x)={2x+5ifx>0x2+2x+5ifx0
f(x)={2ifx>02x+2ifx0
LHL of f(x)=RHL of f(x)
f is differential at x=0.
Hence, B is the correct option.

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