[Tex/LaTex] Area between curves tikz

tikz-pgf

I am trying to plot a graph using tikz, but I can't seem to be able to highlight the areas between the curves. The result should look something like this:

enter image description here

This is the code I have so far: 

\begin{center}
\begin{tikzpicture}[scale=0.8]

\draw[->] (0,-0.5) -- (0,4.5) node[anchor=east] {};
\draw[->] (-0.5,0) -- (9,0) node[anchor=north] {};
\draw   (1,-0.2) node[anchor=north] {$a$}
        (8,-0.2) node[anchor=north] {$b$}       
        ;
\filldraw[fill=black!10](1,0)--(1,2)--(8,2)--(8,0);
\draw [](1,3) parabola bend (2.5,1.5)(4.2,2.4); 
\draw [](4.2,2.4) parabola bend (5.5,3)(8,0); 
\draw[] (1,0)--(1,3);
\end{tikzpicture}
\end{center}

The end result I would like to achieve is to have C and D higlighted in orange, while A and B in a dark grey. Don't worry about the axes labels or else, I mostly need help with the shading.

Thanks in advance!!

Best Answer

For this, I'd suggest you to use the pgfplots package and stacking plots:

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}

\pgfplotsset{compat=newest}

\begin{document}

\pgfmathdeclarefunction{poly}{0}{%
      \pgfmathparse{-x^3+5*(x^2)-3*x-3}%
    }

\begin{tikzpicture}
\begin{axis}[
  domain=-1.2:4.2,
  ymin=-5,
  ymax=10,
  samples=160,
  stack plots=y
]
% draw graph for the first function f
\addplot+[black,thick,mark=none] {poly};
% draw graph of max(g-f, 0) and stack
\addplot+[mark=none,fill=gray!60,draw=cyan] {max(3-(poly),0)} \closedcycle;
% draw graph of min(g-f, 0) and stack
\addplot+[mark=none,fill=orange!70,draw=cyan] {min(3-(poly),0)} \closedcycle;
\end{axis}
\end{tikzpicture}

\end{document}

enter image description here

And with the help lines and labels:

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}

\pgfplotsset{compat=newest}

\begin{document}

\pgfmathdeclarefunction{poly}{0}{%
      \pgfmathparse{-x^3+5*(x^2)-3*x-3}%
    }

\begin{tikzpicture}
\begin{axis}[
  xmin=-2,
  xmax=5,
  ymin=-5,
  ymax=10,
  axis y line=left,
  axis x line=bottom,
  xtick={-1.2,2,4.2},
  xticklabels={$a$,$\zeta$,$b$},
  ytick={3},
  yticklabels={$f(\zeta)$},
  samples=160
]

\addplot[mark=none,help lines,domain=-2:4.2] {3};

% draw graph for the first function f
\addplot+[black,thick,mark=none,domain=-1.2:4.2,stack plots=y] {poly};
% draw graph of max(g-f, 0) and stack
\addplot+[mark=none,fill=gray!60,draw=cyan,domain=-1.2:4.2,stack plots=y] {max(3-(poly),0)} \closedcycle;
% draw graph of min(g-f, 0) and stack
\addplot+[mark=none,fill=orange!70,draw=cyan,domain=-1.2:4.2,stack plots=y] {min(3-(poly),0)} \closedcycle;

\draw[help lines] (axis cs:-1.2,-5) -- (axis cs:-1.2,3);
\draw[help lines] (axis cs:2,-5) -- (axis cs:2,3);
\draw[help lines] (axis cs:4.2,-5) -- (axis cs:4.2,3);
\end{axis}
\end{tikzpicture}

\end{document}

enter image description here

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