Problem in table with fixed width columns and multicolumn

Question

I want to do a diagram following the idea of How to create fixed width table columns with text raggedright/centered/raggedleft?. Using the code

\documentclass{article}

\usepackage{array}
\newcolumntype{C}[1]{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}m{#1}}

\begin{document}

\begin{tabular}{| C{2cm} | C{2cm} | C{2cm} | C{2cm} | C{2cm} | C{2cm} |}
\hline
$f(x)$   & \multicolumn{5}{c|}{+}\\
\hline
$f'(x)$  & \multicolumn{2}{c|}{+} & \multicolumn{2}{c|}{-} & +\\
\hline
$f''(x)$ & - & \multicolumn{2}{c|}{-} & \multicolumn{2}{c|}{+}\\
\hline
\end{tabular}

\end{document}

the widths are ignored:

But adding a multicolumn-less row:

\documentclass{article}

\usepackage{array}
\newcolumntype{C}[1]{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}m{#1}}

\begin{document}

\begin{table}[h]
\begin{tabular}{| C{2cm} | C{2cm} | C{2cm} | C{2cm} | C{2cm} | C{2cm} |}
\hline
$f(x)$   & \multicolumn{5}{c|}{+}\\
\hline
$f'(x)$  & \multicolumn{2}{c|}{+} & \multicolumn{2}{c|}{-} & +\\
\hline
$f''(x)$ & + & \multicolumn{2}{c|}{-} & \multicolumn{2}{c|}{+}\\
\hline
U & V & W & X & Y & Z\\
\hline
\end{tabular}
\end{table}

\end{document}

the widths are OK:

What I'm missing?

Answer 1

I suggest you use (a) an array environment rather than a tabular environment (since the table's contents are all in math mode) and (b) use the w column type to specify the column widths as no line-breaking within columns would seem necessary or desirable. Since the tedious-looking

\multicolumn{2}{w{c}{\dimexpr2\mylen+2\arraycolsep+\arrayrulewidth\relax}|}

expression occurs no fewer four times, I further suggest replacing it with a shortcut macro called, say, \mycol.

\documentclass{article}
\usepackage{array}  % for 'w' column type
\newlength\mylen
\setlength\mylen{1cm} % <-- set the desired usable column width (2cm seems excessive)
% handy shortcut macro:
\newcommand\mycol[1]{%
   \multicolumn{2}{w{c}{\dimexpr2\mylen+2\arraycolsep+\arrayrulewidth\relax}|}{#1}} 
\begin{document}
\[ % start an unnumbered display-math group
\begin{array}{| *{6}{w{c}{\mylen}|} }
\hline
f(x)   & \multicolumn{5}{c|}{+}    \\
\hline
f'(x)  & \mycol{+} & \mycol{-} & + \\
\hline
f''(x) & - & \mycol{-} & \mycol{+} \\
\hline
\end{array}
\]
\end{document}

Answer 2

You can easily construct that array with {NiceMatrix} of nicematrix. That environment is similar to {nicematrix} (of amsmath) but with additionnal features:

• You can specify the width of the columns with the key columns-width.
• You can merge cells (both vertically and horizontally) with the command \Block.
• The key hvlines draws all the rules (except in the blocks created by \Block).

Here is the code.

\documentclass{article}
\usepackage{nicematrix}
\begin{document}
\[\begin{NiceMatrix}[columns-width=1cm,hvlines]
f(x)   & \Block{1-5}{+} \\
f'(x)  & \Block{1-2}{+} && \Block{1-2}{+} && + \\
f''(x) & - & \Block{1-2}{-} && \Block{1-2}{+} \\
\end{NiceMatrix}\]
\end{document}