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Let f(x)=a+b|x|+c|x|^(2), where a,b,c ar...

Let `f(x)=a+b|x|+c|x|^(2)`, where a,b,c are real constants. The, f'(0) exists if

A

b=0

B

c=0

C

a=0

D

b=c

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`f(x)=a+b|x|+c|x|^(2)`
`Rightarrow f(x)=a+b|x|+cx^(2)`
Clearly, f(x) will not be differentiable at x=0 if |x| remains in the expression for f(x). Thus, f(0) exists, if b=0
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