Is there such thing as “p{height}”

Question

I am making a table right now and it's really annoying that items in my cell are getting crunched

\begin{center}
\begin{tabular}{|c| c | c|}
Critical Points $P_0$ & $f(P_0)$ & Conclusion \\ 
\hline
(0,0,1)     & 0 & Local Extrema\\ \hline
(0,0,-1)    & -2  & Absolute minimum \\ \hline
$\left ( 0,0,\frac{1}{2} \right ) $ & $\frac{1}{4}$ & Local Extrema \\  \hline

$(0,0, \frac{\sqrt{12}}{5})$ & $\frac{8}{5}$ & Absolute maximum \\ \hline

$(0,0, -\frac{\sqrt{12}}{5})$ & $\frac{8}{5}$ & Absolute maximum \\ 
\end{tabular}
\end{center}

My fractions are getting crushed and there is no such thing as "p{height}" to fix.

Answer 1

Instead of increasing the vertical space for rows, I propose you some changes:

1. Don't use \frac{a}{b} but simply a/b; this increases readability.
2. Use the features provided by the booktabs and array packages.

3. Eliminate the vertical rules.

   \documentclass{article}
   \usepackage{amsmath}
   \usepackage{array}
   \usepackage{booktabs}
   
   \begin{document}
   
   \begin{center}
   \begin{tabular}{*{2}{>{$}c<{$}} c}
   \toprule
   \multicolumn{1}{c}{Critical Points $P_0$} & f(P_0) & Conclusion \\ 
   \cmidrule(r){1-1}\cmidrule(lr){2-2}\cmidrule(l){3-3}
   (0,0,1)     & 0 & Local Extrema\\ 
   (0,0,-1)    & -2  & Absolute minimum \\ 
   (0,0,1/2 )  & 1/4 & Local Extrema \\ 
   (0,0,\sqrt{12}/5) & 8/5 & Absolute maximum \\ 
   (0,0, -\sqrt{12}/5) & 8/5 & Absolute maximum \\ 
   \bottomrule
   \end{tabular}
   \end{center}
   
   \end{document}
   

If, for some reason, using array and booktabs is not possible, my first and third recommendations still apply and you can change \arraystretch; something along these lines:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{center}
\renewcommand\arraystretch{1.2}
\begin{tabular}{c c c}
\hline
Critical Points $P_0$ & $f(P_0)$ & Conclusion \\ 
\hline
$(0,0,1)$     & $0$ & Local Extrema\\ 
$(0,0,-1)$   & $-2$  & Absolute minimum \\ 
$(0,0,1/2 )$  & $1/4$ & Local Extrema \\ 
$(0,0,\sqrt{12}/5)$ & $8/5$ & Absolute maximum \\ 
$(0,0, -\sqrt{12}/5)$ & $8/5$ & Absolute maximum \\ 
\hline
\end{tabular}
\end{center}

\end{document}

Answer 2

The package cellspace offers a simple way to get the correct height:

\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage{booktabs}
\usepackage{cellspace}
\addtolength\cellspacetoplimit{3pt}
\addtolength\cellspacebottomlimit{3pt}
\begin{document}

\begin{center}
\begin{tabular}{>{$}c<{$}>{$}Sc<{$}c}
\toprule
\multicolumn{1}{c}{Critical Points $P_0$} & f(P_0) & Conclusion \\ 
\cmidrule(r){1-1}\cmidrule(lr){2-2}\cmidrule(l){3-3}
(0,0,1)     & 0 & Local Extrema\\ 
(0,0,-1)    & -2  & Absolute minimum \\ 
(0,0,1/2 )  & \dfrac14 & Local Extrema \\ 
(0,0,\sqrt{12}/5) & \dfrac85 & Absolute maximum \\ 
(0,0, -\sqrt{12}/5) & \dfrac85 & Absolute maximum \\ 
\bottomrule
\end{tabular}
\end{center}

\end{document}