> [!NOTE] Theorem 1 > Let $Z:[t_{0},T] \to \mathbb{R}$ be a nonnegative [[Fréchet Differentiation|differentiable]] function, where $[t_{0},T]$ is an [[Real intervals|interval]], for which there exists a constant $c$ such that for all $t\in [t_{0},T],$ $Z'(t) \leq c Z(t).$Then for all $t\in [t_{0},T],$ $Z(t)\leq Z(t_{0})e^{c(t-t_{0})}$ **Proof**: ... # Applications See [[Uniqueness Theorem for Explicit First Order Initial Value Problem]].