# Convex Function

A function \(f\) is convex if its values between any two points upon its graph do not lie above the straight line \(g\) connecting those points. Specifically

If they lie below that straight line except at those points then it is is known as a

\[
g(x) = \frac{x-x_0}{x_1-x_0} \times f\left(x_1\right) + \frac{x_1-x}{x_1-x_0} \times f\left(x_0\right)\\
\forall x \in \left[x_0, x_1\right] \quad f(x) \leqslant g(x)
\]

where \(\in\) means *within*, the square brackets represent a closed interval and \(\forall\) is the universal quantifier.If they lie below that straight line except at those points then it is is known as a

*strictly*convex function.