Show that there is no differentiable function $f : \mathbb{R} \longrightarrow \mathbb{R}$ such that $f(0) = 1$ and $f^{\prime}(x) \geq (f(x))^{2}$ for every $x \in \mathbb{R}$.
Show that there is no differentiable function $f : \mathbb{R} \longrightarrow \mathbb{R}$ such that $f(0) = 1$ and $f^{\prime}(x) \geq (f(x))^{2}$ for every $x \in \mathbb{R}$.