I have following doubt.
Mean value theorem states for any continuous differential function $f$ over $(a,b)$,
There exists some $c$ such that $f(b)-f(a)=f'(c)(b-a)$
My question is for any $d$, can we find an $i$ and $j$ such that
$f'(d)<=\frac{(f(i)-f(j))}{(i-j)}?$ Can we extend the argument to multi-variable function? Thanks