I have tick marks at $\pm (2/3)\sqrt{3}$ on the x-axis. How do I prevent the typesetting of the labels for these tick marks?
\documentclass{amsart}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{tikz}
\usetikzlibrary{calc,intersections}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\begin{document}
\begin{tikzpicture}
\begin{axis}[width=3.5in, height=3.5in, axis lines=middle, clip=false,
axis lines=middle, clip=false,
xmin=-2.5251,xmax=2.4567,
ymin=-3,ymax=8,
restrict y to domain=-3:8,
xtick={-1.1547, 1.1547}, ytick={\empty},
axis line style={latex-latex},
xlabel=$x$,ylabel=$y$,
axis line style={shorten >=-12.5pt, shorten <=-12.5pt},
xlabel style={at={(ticklabel* cs:1)}, xshift=12.5pt, anchor=north west},
ylabel style={at={(ticklabel* cs:1)}, yshift=12.5pt, anchor=south west}
]
\addplot[samples=501, domain=-2.5251:2.4567] {x^3 - 4*x + 3};
\addplot[samples=2, latex-latex, dashed, domain=-2.5251:2.4567] {-x + 5};
\fill[blue] (-1, 6) circle [radius=1.5pt];
%P = (2.25, 5.390625) is a point on the graph of y = x^{3} - 4x + 3.
%The slope of the tangent line at P is 11.1875. An equation for the
%tangent line is y = 11.1875x -19.78125. Q = (1.786816, 0) is the
%x-intercept for the line.
\coordinate (P) at (2.25, 5.390625);
\coordinate (Q) at (1.786816, 0);
\end{axis}
%A "pin" is drawn to the cubic polynomial.
\draw[draw=gray, shorten <=1mm, shorten >=1mm] (P) -- ($(P)!0.75cm!90:(Q)$);
\node[anchor=west, inner sep=0, font=\footnotesize] at ($(P)!0.75cm!90:(Q)$){\makebox[0pt][l]{$y = x^{3} - 4x + 3$}};
\end{tikzpicture}
\end{document}

xtick={-1.1547, 1.1547}which of course then also plots them. If you don't want to show any xticks, then also useytick={\empty}as you did for the yticks ... – Stefan Pinnow Mar 11 '17 at 15:06x-axis; I do not want-1.1547and1.1547typeset under the tick marks. – A gal named Desire Mar 11 '17 at 16:09xticklabels={}to theaxisoptions. Is that what you want? (Just showing the ticks without labels.) – Stefan Pinnow Mar 11 '17 at 16:24