MathDB

Let us consider a triangle

\Delta{PQR}

in the co-ordinate plane. Show for every function

f: \mathbb{R}^2\to \mathbb{R}\;,f(X)=ax+by+c

where

X\equiv (x,y) \text{ and } a,b,c\in\mathbb{R}

and every point

A

\Delta PQR

or inside the triangle we have the inequality: \begin{align*} & f(A)\le \text{max}\{f(P),f(Q),f(R)\} \end{align*}

Problem Statement