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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

`mu=0`

B

`v=0`

C

`lambda=0`

D

`mu=v`

Text Solution

Verified by Experts

The correct Answer is:
A
`f(x)= lambda +mu|x| +v|x|^(2)`
`f(x)={(lambda+mux+vx^(2)",",x ge 0),(lambda-mux+vx^(2)",",x lt 0):}`
`f'(x)={(mu+2vx",",x gt 0),( -mu+2vx",", x lt 0):}`
If f'(0) exist then `mu=0`
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