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

tikz-pgf

How I can draw a convex function in latex like this?

A tikz solution

\documentclass[tikz,border={15mm 15mm 15mm 15mm},]{standalone}
\usepackage{pgfplots}
\pgfplotsset{plot coordinates/math parser=false}
\pgfplotsset{
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
}
\pgfplotsset{
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
}
\usetikzlibrary{
arrows.meta,
intersections,
}

\begin{document}

\begin{tikzpicture}
\begin{axis}[width=5in,axis equal image,
axis lines=middle,
xmin=0,xmax=8,
xlabel=$x$,ylabel=$y$,
ymin=-0.25,ymax=4,
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);
\end{axis}
\end{tikzpicture}

\end{document}