Proving an inequality between functions: are the bounds sufficient if both strictly increase and are concave? I would like to show that 
$$f(n) > g(n)$$ for all $n$ within a certain range.
If I can show that both $f(n)$ and $g(n)$ are strictly increasing with $n$, and that both are strictly concave, and that $f(n) > g(n)$ at both the lower and upper bounds of $n$, is that sufficient?

No. Consider, for example, $f(x)=1+12x-x^2$ and $g(x)=20x-10x^2$ between $0$ and $1$.
Plotted by Wolfram Alpha.
