My professor posted this question as a supplement to our exercises in Rudin. As a disclaimer, this class has been difficult for me in the past, so forgive me if I've missed any really simple steps... Here is the question:
"Let $f:[0, \infty)\to R$ be given, such that $f$ is continuous on $[0,\infty)$. Suppose $f(0)=0$, where $f$ is differentiable on $(0,\infty)$, and $f'$ is monotonic increasing on $(0,\infty)$. Prove that f is supperadditive on $[0,\infty)$ meaning that $f(x+y)\ge f(x)+f(y)$ for all $x, y \in [0,\infty)$."
What does it mean when the first derivative is monotonic increasing? Does that tell me $f''\ge0$ or is that even useful information?
Where does one begin on problems like this? If not a solution to the problem, general problem solving advice for real analysis proofs would be much appreciated. - Thanks.