Question

If $y=f\left(x\right)$ is an odd differentiable function defined on $(-\infty ,\infty )$ such that $f^{\prime }\left(3\right)=-2$ then $f^{\prime }(-3)$ equals-

• A. $4$
• B. $2$
• C. $-2$
• D. $0$

Answer 1

The correct option is C $-2$

Given that f is odd function

$\Rightarrow f(-x)=-f\left(x\right)$

$\Rightarrow (-1)f^{\prime }(-x)=-f^{\prime }\left(x\right)$

$\Rightarrow f^{\prime }(-x)=+f^{\prime }\left(x\right)$

let $x=3$

$\Rightarrow f^{\prime }(-3)=f^{\prime }\left(3\right)$

$=-2$