Can anyone help me prove the convexity of this rational function? The man who proved the convexity of function used these facts. But I don't know this fact is correct or not. Here are the facts and function:
1. As N increases, f(N) goes to infinity, That implies that there must be a minima (either at N=0 or somewhere else with a finite N)
2. There cannot be more than one (positive) minima since we're dealing with second order equation.
a,b,c,d,e,f,g is constants. and . I guess the second order equation means that between the leading coefficient of the numerator and the denominator is 2.
Are these facts correct? I think fact 1 is no problem, but fact 2 is correct or not.
I am waiting for any answers.