Question

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

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is C $2$

The differentiable odd function gives even function on differentiation.
Hence if $f\left(x\right)$ is odd then $f^{\prime }\left(x\right)$ is even.
Thus
$f^{\prime }\left(x\right)=f^{\prime }(-x)$
Now it is given that $f^{\prime }\left(3\right)=2$, hence $f^{\prime }(-3)=f^{\prime }\left(3\right)=2$