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Let f(x) be a function which is differen...

Let f(x) be a function which is differentiable any number of times and `f(2x^(2)-1)=2x^(3)f(x), AA x in R`. Then `f^((2010))(0)=` (Here `f^((n))(x)=n^(th)` order derivative of f at x)

A

`-1`

B

1

C

0

D

data is insufficient

Text Solution

Verified by Experts

The correct Answer is:
C
Replace x by `-x`
`therefore" "f(2x^(2)-1)=-2x^(3)f(-x)`
`" "2x^(3)f(x)=-2x^(3)f(-x)`
`rArr" "f(-x)=-f(x)`
`therefore" f(x) or odd function"`
`therefore" "f^((n))(0)=0`, when n is even
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