- 338

- 0

where f(x) and g(x) are positive functions.

I suspect that u(x) < 0 in the domain 0 < x < 1. How do I go proving this.

I have try proving by contradiction. Assuming first u > 0 but I can't deduce that u" > 0 which contradict that u has a maximum in the domain. Or because my conjecture is wrong