Let $a$,$b$ be positive real numbers such that $a. Show that $f(x)$ is non-negative for all $x>0$ where
$f(x)= \phi(a-x)-\phi(b+x)$ where $\phi$ is the standard normal PDF.
So far I have that $f(0)>0$ and that
$f'(x)=(a-x)\phi(a-x)+(b+x)\phi(b+x)$
and then I get stuck