Question

If $f\left(x\right)$ is an odd function and $f^{\prime }\left(x\right)$ exists then $f^{\prime }\left(e\right)-f^{\prime }(-e)$ is

• A. $0$
• B. $e$
• C. $\frac{1}{e}$
• D. $1$

Answer 1

The correct option is A $0$

As $f\left(x\right)$ is an odd function, then
$f\left(x\right)=-f(-x)\Rightarrow f^{\prime }\left(x\right)=-f^{\prime }(-x)\cdot -1=f^{\prime }(-x)$
$\Rightarrow f^{\prime }\left(e\right)=f^{\prime }(-e)\Rightarrow f^{\prime }\left(e\right)-f^{\prime }(-e)=0$