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I have the inequality

$f''(x)x + f'(x) \leq 0$

Also, $f''(x)<0$ and $f'(x)>0$ and $x \in R^+$. And I need to figure out when it is true. I know it is a fairly general question, but I couldn't find any information in several textbooks I have skimmed. Also, I am not sure if integrating would require a sign reversal or not, so I cant go ahead and try to manipulate it my self.

Any help or mention of a helpful source would be much appreciated.

edit: forgot to mention $f(x)\geq 0$ for every $x \in R^+$

2 Answers 2