Question 89
Find all differentiable functions $f: [0, \infty) \to \mathbb{R}$, $f(0) = 0$, so that:
i) $f'$ is strictly positive and increasing;
ii) $\int_0^1 (f'(x))^2 dx \ge f(x+f(x))-f(x)$, for every $x \in [0, \infty)$.
i) $f'$ is strictly positive and increasing;
ii) $\int_0^1 (f'(x))^2 dx \ge f(x+f(x))-f(x)$, for every $x \in [0, \infty)$.