![如何制作像这样的图形上的切线?](https://linux22.com/image/415874/%E5%A6%82%E4%BD%95%E5%88%B6%E4%BD%9C%E5%83%8F%E8%BF%99%E6%A0%B7%E7%9A%84%E5%9B%BE%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%88%87%E7%BA%BF%EF%BC%9F.png)
我在这里尝试了一次又一次,但无法进一步...谢谢帮助!
\documentclass{article}
\usepackage{lmodern}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{calc, hobby}
\tikzset{
tangent/.style = {
in angle={(180+#1)},
Hobby finish,
designated Hobby path=next,
out angle=#1
}
}
\begin{document}
\begin{figure}[htbp]
\centering
\begin{tikzpicture}
\coordinate (y) at (0,5);
\coordinate (x) at (6,0);
\coordinate (sp0) at (2.75,0);
\coordinate (ep0) at (4.75,3);
\coordinate (csp0) at (3.5,2);
\coordinate (cep0) at (3.75,-0.5);
\coordinate (sp1) at (ep0);
\coordinate (ep1) at (5.5,4);
\coordinate (csp1) at (5.25,5);
\coordinate (cep1) at (5.25,2);
\coordinate (sp2) at (sp0);
\coordinate (ep2) at (-0.25,-0.65);
\coordinate (csp2) at (1.5,0);
\coordinate (cep2) at (1.5,0);
\draw[<->] (y) node[left] {$y$} -- (0,0) -- (x) node[below] {$x$};
% Using \pgfmathanglebetweenpoints to calculate the angle for tangent
% tangent takes a degree unit angle
\pgfmathanglebetweenpoints{\pgfpointanchor{cep0}{center}}{\pgfpointanchor{ep0}{center}}
\let\angle=\pgfmathresult
\draw (ep2) to [curve through ={(sp0) .. ([tangent=\angle]ep0)}] (ep1) ;
\draw[dashed] (cep0) -- (csp1);
\draw[dotted] let \p1 = (ep0) in (ep0) -- (0,\y1);
\draw[dotted] let \p1 = (ep0) in (ep0)-- (\x1,0);
\draw let \p1 = (ep0) in (\x1,1pt) -- (\x1,-3pt) node[anchor=north] {$x_0$};
\draw let \p1 = (cep0) in (\x1,1pt) -- (\x1,-3pt) node[anchor=north] {$x_1$};
\draw let \p1 = (ep0) in (1pt,\y1) -- (-3pt,\y1) node [anchor=east] {$f(x_0)$};
\end{tikzpicture}
\caption{Newtons metode}
\label{fig:newtonsmetode}
\end{figure}
\end{document}
答案1
John Kormylo 已经提到,如果使用显式函数,则只需计算其切线的斜率即可。
\documentclass{article}
\usepackage{lmodern}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{calc,intersections}
\begin{document}
\begin{figure}[htbp]
\centering
\begin{tikzpicture}[>=stealth,
declare function={f(\x)=-0.35+5*exp(\x/2)/exp(3);
fprime(\x)=2.5*exp(\x/2)/exp(3);},
dot/.style={circle,fill,inner sep=1pt},
every pin edge/.style={thin}]
\path (0,0) coordinate[label=below left:{$O$}] (O)
(0,5) coordinate (y) (6,0) coordinate (x);
\draw[->,name path=x-axis] (-0.5,0) -- (x) node[below] {$x$};
\draw[->] (0,-0.5) -- (y) node[left] {$y$};
\draw[semithick,cyan,name path=curve] plot[variable=\x,domain=0.1:6,smooth]
(\x,{f(\x)}) (5.8,{f(6)})node[black,left]{$y=f(x)$};
\draw[red,dashed] (5.5,0) coordinate(x0) -- (5.5,{f(5.5)}) coordinate(p0)
($(p0)+(-1,{-1*fprime(5.5)})$) coordinate(p0');
\draw[red,dashed] (intersection of p0--p0' and O--x) coordinate (x1)
let \p1=(x1) in \pgfextra{\pgfmathsetmacro{\myx}{\x1/1cm}}
(x1) -- (\myx,{f(\myx)}) coordinate(p1)
($(p1)+(-1,{-1*fprime(\myx)})$) coordinate(p1');
\draw[red,dashed] (intersection of p1--p1' and O--x) coordinate (x2)
let \p1=(x2) in \pgfextra{\pgfmathsetmacro{\myx}{\x1/1cm}}
(x2) -- (\myx,{f(\myx)}) coordinate(p2)
($(p2)+(-1,{-1*fprime(\myx)})$) coordinate(p2');
\path (intersection of p2--p2' and O--x) coordinate (x3)
(x3) node[draw,label=below:{$x_{3}$}] {}
foreach \X [count=\Y] in {0,...,2}
{(x\X) node[draw,label=below:{$x_{\X}$}] {}
(x\Y) edge[red,shorten >=-1em,shorten <=-1ex] (p\X)
\ifnum\X=0
(p\X) node[dot,cyan,label={[black]left:{$(x_{\X},f(x_{\X}))$}}] {}
\else
(p\X) node[dot,cyan,pin={[black]90:{$(x_{\X},f(x_{\X}))$}}] {}
\fi
};
\path[name intersections={of=curve and x-axis,by=i}]
(i) node[cyan,draw,fill,
,pin={[black,align=center]90:point\\ sought}](in){};
\end{tikzpicture}
\caption{Newtons metode}
\label{fig:newtonsmetode}
\end{figure}
\end{document}