\begin{definition}[Definition:Convex Real Function/Definition 2]
Let $f$ be a real function which is defined on a real interval $I$.
$f$ is '''convex on $I$''' {{iff}}:
:$\forall x_1, x_2, x_3 \in I: x_1 < x_2 < x_3: \dfrac {f \left({x_2}\right) - f \left({x_1}\right)} {x_2 - x_1} \le \dfrac {f \left({x_3}\right) - f \left({x_2}\right)} {x_3 - x_2}$
Hence a geometrical interpretation: the slope of $P_1 P_2$ is less than or equal to that of $P_2 P_3$:
:500px
\end{definition}