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 strictly concave function.
\[
g(x) = \frac{x-x_0}{x_1-x_0} \times f\left(x_1\right) + \frac{x_1-x}{x_1-x_0} \times f\left(x_0\right)\\
\forall x \in \left[x_0, x_1\right] \quad f(x) \geqslant g(x)
\]
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.
Gallimaufry
This site requires HTML5, CSS 2.1 and
JavaScript 5 and has been tested with
|
Chrome 26+ |
|
Firefox 20+ |
|
Internet Explorer 9+ |
