For $D\subset R \rightarrow R$, $f$ is log concave iff $f''f\leq (f')^2$ for all $x\in D$

Question

So I know that a function $f: D\subset R^n \rightarrow R$ is called log-concave if $f(x)>0$ for all $x\in D$ and $log f$ is concave.

I'm stuck on showing that for $D\subset R \rightarrow R$, $f$ is log concave iff $f''f\leq (f')^2$ for all $x\in D$.

Answer 1

$\log f$ is concave iff $(\log f)''\le0$ with $$ (\log f)'' = \frac d{dx} \frac f{f'} = 1 - \frac {ff''}{(f')^2} $$