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. $4$

Answer 1

The correct option is C $2$

Since the function is an odd function, thus,
$f\left(x\right)=-f(-x)f^{\prime }\left(x\right)=f^{\prime }(-x)$
Substitute $-3$ for $x$ in the above equation.
$f^{\prime }(-3)=f^{\prime }\left(3\right)=2$