[Tex/LaTex] How one can draw a convex function


enter image description hereHow I can draw a convex function in latex like this?

Best Answer

A tikz solution

\documentclass[tikz,border={15mm 15mm 15mm 15mm},]{standalone}
\pgfplotsset{plot coordinates/math parser=false}
    every non boxed x axis/.style={
        xtick align=center,
        enlarge x limits=true,
        x axis line style={line width=0.8pt, -latex}
    every boxed x axis/.style={}, enlargelimits=false
    every non boxed y axis/.style={
        ytick align=center,
        enlarge y limits=true,
        y axis line style={line width=0.8pt, -latex}
    every boxed y axis/.style={}, enlargelimits=false


\begin{axis}[width=5in,axis equal image,
    axis lines=middle,
    xtick={\empty},ytick={\empty}, axis on top

\addplot[thick,domain=0.25:7,blue,name path = A]  {-x/3 + 2.75} coordinate[pos=0.4] (m) ;
\draw[thick,blue, name path =B] (0.15,4) .. controls (1,1) and (4,0) .. (6,2) node[pos=0.95, color=black, right]  {$f(x)$} coordinate[pos=0.075] (a1)  coordinate[pos=0.95] (a2);
\path [name intersections={of=A and B, by={a,b}}];

\draw[densely dashed] (0,0) -| node[pos=0.5, color=black, label=below:$a$] {}(a1);
\draw[densely dashed] (0,0) -| node[pos=0.5, color=black, label=below:$x_{1}$] {}(a);
\draw[densely dashed, name path=D] (3,0) -|node[pos=0.5, color=black, label=below:$\lambda x_{1}+ (1-\lambda)x_{2}$] {} node[pos=1, fill,circle,inner sep=1pt] {}(m);
\draw[densely dashed] (0,0) -|node[pos=0.5, color=black, label=below:$x_{2}$] {}(b);
\draw[densely dashed] (0,0) -|node[pos=0.5, color=black, label=below:$b$] {}(a2);

\path [name intersections={of=B and D, by={c}}] node[fill,circle,inner sep=1pt] at (c) {}; 

\node[anchor=south west, text=black] (d) at (0.75,3) {$f[\lambda x_{1}+(1-\lambda)x_{2}]$};
\node[anchor=south west, text=black] (e) at (5,2.5) {$\lambda f(x_{1})+(1-\lambda)f(x_{2})$};
\draw[-{Latex[width=4pt,length=6pt]}, densely dashed] (d) -- (c);
\draw[-{Latex[width=4pt,length=6pt]}, densely dashed] (e) -- (m);


enter image description here