Thanks for that! I'll try that.
But you agree with my intuition that it is suitable to utilise Hessian approach to this exercise? Is there any other way to conclude that it is always true with given conditions?
Hello everybody! I am new here and probably going to visit here pretty often in the future. Sometimes I do not get very clear answer from the lecturers so I hope to get more sensible answers from PF.
Homework Statement
I need to show that x^y > y^x whenever y > x ≥ e.
The Attempt at a...
I have a question considering the applicability of Hessian matrix.
So, Can I use Hessian to prove that x^y > y^x whenever y > x >= e.
At first I start by multiplying by ln() => y*ln(x) > x*ln(y)
Is it enough, if I take g(x,y) such that g(x,y) = y*ln(x) - x*ln(y) > 0 and show det(H(g)) < 0...