# Concave Function

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

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

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

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

*strictly*concave function.