I'm trying to study the sign of an expression, having information on some of my parameters. I don't know how to code these conditions. For example, I want to know when this expression:

    k [2(a'[x])^2 - a[x]a''[x]] / (a[x]^2) 

is positive given that `k > 0`, `x > 0` and that my function `a` is positive and increasing for all `x > 0`. 

So basically, since `a''[x]` is the only term of the equation that I don't know anything about, I want *Mathematica* to give me:

    (* a''[x] < a'[x]^2/a[x] *)