Styling part of a monotony table

Question

I am reading the tikz tab manual but I cannot find an answer.

MWE

\documentclass[11pt]{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pgf,tikz}
\usepackage{tkz-tab}
\usetikzlibrary{shapes,snakes,arrows,backgrounds}
\usetikzlibrary{scopes,svg.path,shapes.geometric,shadows}

\begin{document}
\begin{tikzpicture}
\tikzset{arrow style/.style   = {black,
->,
>->           = latex’,thick ,
shorten >   =  5pt,
shorten <   =  5pt}}
\tkzTabInit[espcl=2.5]{$x$ /1,$f'$ /1, $f$ /2 }
{$0$ ,$e$, $+\infty$}
\tkzTabLine{ d,- , z,+ ,}
\tkzTabVar{ D+/$+\infty$ , -/$f(e)=2$/ , +/$+\infty$}%
\end{tikzpicture}
\end{document}

produces

and my desired output would be the following:

using the style \tikzset{h style/.style ={pattern=north west lines}}, Actually , I had placed h and H here but to no avail.

\tkzTabLine{ h,d,- , z,+ ,}
\tkzTabVar{ H,D+/$+\infty$ , -/$f(e)=2$/ , +/$+\infty$}%

Truth be told I can't follow some guidelines of the manual because it is in French and since I don't know French I cannot get useful information about the functionality of some code. Any help?

Answer 1

Something like this?

I'm afraid I don't know French either.

\documentclass[border=10pt,multi,tikz]{standalone}
\usepackage{tkz-tab}
\begin{document}
\begin{tikzpicture}
  [
    arrow style/.style = {
      black,
      ->,
      >-> = latex',
      thick,
      shorten > = 5pt,
      shorten < = 5pt,
    },
  ]
  \tkzTabInit[espcl=2.5]{$x$ /1, $f'$ /1, $f$ /2 }
  {,$0$ ,$e$, $+\infty$}
  \tkzTabLine{ d,h,d,- , z,+ ,}
  \tkzTabVar{ +DH/,D+/$+\infty$ , -/$f(e)=2$/ , +/$+\infty$}%
\end{tikzpicture}
\end{document}