I would like to study the sign of an expression including a function and its 1st and 2nd derivatives. My function is positive and strictly increasing but I don't want to have to specify its form. I can't find a way to make these 2 statements, so that the condition would be on the 2nd derivative. I tried "Assumptions", "ForAll[x, f[x]>0 && f'[x]>0]","/;{f[x]>0,f'[x]>0}","If"..but nothing works. I didn't succeed either on programming easier examples like:
if f'[x]>0 and x<y, then f[x]<f[y] -> True
or 2+a>2/;a>0 -> True
Thank you very much for your help