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If y=f(x) is an odd differentiable funct...

If `y=f(x)` is an odd differentiable function defined on `(-oo,oo)` such that `f^(prime)(3)=-2,t h e n|f^(prime)(-3)|` equals_________.

A

1

B

2

C

-2

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
Since f(x) is an odd differentiable function defined on R. Therefore,
`f(-x)=-f'(x)" ""tor all "x in R`
Differentiating both sides w.r.t.x, we get
`-f'(-x)=-f'(x)" "" for all "x in R`
`impliesf'(-x)=f'(x)" "" for all "x in R`
`implies" "f'(-3)=f'(3)=-2`
ALITER We know that the derivative of a differentiable odd function is an even function. Therefore, `f'(x)` is an even function. Hence,
`f'(-3)=f'(3)=-2`
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