I read that, a function $f$ is concave if and only if,
$f(a+t) - f(a) \geq f(b+t)-f(b), \forall a,b, 0< a < b, t>0$
How do we get this result ?. It does not sound very evident from the definition of concave functions. Does this mean that, for any convex function
$f(a+t) - f(a) \leq f(b+t)-f(b), \forall a,b, 0< a < b, t>0$