Let a function $ \phi : \mathbb{R} \rightarrow \mathbb{R^n}$ that satisfies $|\phi´(t)| \leq L|\phi(t)| $ for some $L$ constant. Show that $|\phi(t)| \leq |\phi(0)| + L\int_{0}^{t} |\phi(t)| dt$ for $t\geq 0$
I think i have to use the Mean value theorem. But its not clear to me how to use it.