I would like to change the discretization tikz uses in order to get a smoother graph.
\documentclass[article]{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat = newest} % loads newest improved settings
\begin{document}
\begin{tikzpicture}
\begin{axis}[scale only axis, xlabel = x, xmin = 0, xmax = 4, ylabel = y, ymax = 40, ymin = 0, ytick pos=left]
\addplot [black, domain=0:3.5] {25*x^0.2};
\end{axis}
\end{tikzpicture}
\end{document}


\addplot [black, domain=0:3.5, smooth] {25*x^0.2};:-) – Zarko Nov 06 '17 at 14:35