Properties concave functions

Question

Is is true that if $f(x)$ is a concave function of $x$ with domain $C$, then $f'(a) \leq \frac{f(a)}{a}$ for any $a \in C$, where $f'(a)$ denotes the derivative of $f(x)$ with respect to $x$ evaluated at $a$? In positive case, can you show it?

Answer 1

It is not true. Consider a typical concave function $f(x)=-x^2$. Then $f'(-1)=2>1=\frac{-1}{-1}=\frac{f(a)}{a}$.