Question

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

• A. $0$
• B. $1$
• C. $2$
• D. $-2$

Answer 1

The correct option is C $2$

If $f\left(x\right)$ is an odd function then $f\left(x\right)=-f(-x)$

Now differentiate above equation both sides

$f^{\prime }\left(x\right)=f^{\prime }(-x)$, using chain rule

Now substitute $x=3$

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

$\Rightarrow 2=f^{\prime }(-3)$

$\therefore f^{\prime }(-3)=2$