The main results of this work are three sufficient conditions for the (1) stability, (2) uniform asymptotic stability in the large and (3) instability, of the equilibrium point $x = 0$ of the system of differential equations: $\dot x = f(t,x)$, $f(t,0) = 0$. Stated roughly these conditions are: The point $x = 0$ is (1) stable if $x'f(t,x)$ is a concave function of x, (2) uniformly asymptotically stable in the large if $x'f(t,x)$ is a concave function of x is a strictly concave function of x, and (3) unstable if $x'f(t,x)$ is a strictly convex function of x. These results are obtained by using the stability and instability criteria of Liapunov and properties of concave and convex functions.