pgfplots 中的曲线下面积

Question

\begin{figure}[H]
\begin{center}
\begin{tikzpicture}
\begin{axis}[xticklabels={},yticklabels={},axis x line=center, axis y 
line=center, xlabel={$x$}, ylabel={$y$}, xlabel style={right}, ylabel style= 
{above},ticks=none]
\addplot[color=brown,domain=-0.1:1.1,samples=100]{(2*x-1)^4};
\addplot[domain=7/8:1.1,samples=100]{8*x-7};
\end{axis}
\node [] at (3.4,0.2) {$P$};
\end{tikzpicture}
\caption{Graph of $y = (2x-1)^4$ (brown) and the tangent function (black) at 
the point $(1,1)$.}
\end{center}
\end{figure}

大家好，我不太清楚如何为切线函数和曲线之间的区域着色。如果能得到帮助就太好了！！！

Answer 1

欢迎使用 TeX.SE！一种方法是使用fillbetween。

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{backgrounds}
\begin{document}
\begin{tikzpicture}
\begin{axis}[xticklabels={},yticklabels={},axis x line=center, axis y 
line=center, xlabel={$x$}, ylabel={$y$}, xlabel style={right}, ylabel style= 
{above},ticks=none]
\addplot[color=brown,domain=-0.1:1.1,samples=100,name path=curve]{(2*x-1)^4};
\addplot[domain=7/8:1.1,samples=101,name path=tangent]{8*x-7+0.01};
\draw[name path=axis] (0,0) -- (7/8,0);
\node [anchor=south] at (0.5,0) {$P$};
\end{axis}
\path [name path=aux1,%draw=blue,%->,fill=orange,
intersection segments={of=curve and axis,
    sequence={R3[reverse]--L3}}];
\begin{scope}[on background layer]      
 \path [fill=orange,
 intersection segments={of=aux1 and tangent,
     sequence={L1--R1}}];
\end{scope}
\end{tikzpicture}
\end{document}

但在这种情况下，您当然可以在没有的情况下进行填充fillbetween。

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\usetikzlibrary{backgrounds}
\begin{document}
\begin{tikzpicture}
\begin{axis}[xticklabels={},yticklabels={},axis x line=center, axis y 
line=center, xlabel={$x$}, ylabel={$y$}, xlabel style={right}, ylabel style= 
{above},ticks=none]
\addplot[color=brown,domain=-0.1:1.1,samples=101]{(2*x-1)^4};
\addplot[domain=7/8:1.1,samples=2]{8*x-7};
\node [anchor=south] at (0.5,0) {$P$};
\begin{scope}[on background layer]      
 \fill[orange] plot[variable=\x,domain=0.5:1.1,samples=51] (\x,{(2*\x-1)^4})
 -- (1.1,{8*1.1-7})-- (7/8,0);
\end{scope}
\end{axis}
\end{tikzpicture}
\end{document}