How To Draw A Tangent To A Curve

By adaption Jake's code given here to a similar problem, you can add a tangent line at any x coordinate "automatically". This also should work for every \addplot command you state, also the \addplot coordinates command given in the question.

          % used PGFPlots v1.13 and TikZ v3.0.1a \documentclass[border=2mm]{standalone} \usepackage{xcolor}     \colorlet{Curve}{red!75!black}     \colorlet{Tangent}{blue!75!black} \usepackage{pgfplots}     \pgfplotsset{compat=1.10}     \usetikzlibrary{         calc,         intersections,         math,     }     \makeatletter         \def\parsenode[#1]#2\pgf@nil{%             \tikzset{label node/.style={#1}}             \def\nodetext{#2}         }         \tikzset{             % define style for the points             Point/.style={                 shape=circle,                 inner sep=0pt,                 minimum size=3pt,             },             add node at x/.style 2 args={                 name path global=plot line,                 /pgfplots/execute at end plot visualization/.append={                         \begingroup                         \@ifnextchar[{\parsenode}{\parsenode[]}#2\pgf@nil                     \path [name path global = position line #1-1]                         ({axis cs:#1,0}|-{rel axis cs:0,0}) --                         ({axis cs:#1,0}|-{rel axis cs:0,1});                     \path [xshift=1pt, name path global = position line #1-2]                         ({axis cs:#1,0}|-{rel axis cs:0,0}) --                         ({axis cs:#1,0}|-{rel axis cs:0,1});                     \path [                         name intersections={                             of={plot line and position line #1-1},                             name=left intersection                         },                         name intersections={                             of={plot line and position line #1-2},                             name=right intersection                         },                         label node/.append style={pos=1}                     ] (left intersection-1) -- (right intersection-1)                         node [label node]{\nodetext};                     % ---------------------------------------------------------                     % draw the tangent line from a bit right of the point on                     % the curve to the intersection with the ordinate                     % and draw the corresponding points                     \draw [Tangent] let                         \p1=($ (left intersection-1) - (right intersection-1) $),                         \p2=($ (left intersection-1)!sign(#1)*5mm!(right intersection-1) $),                         \p3=($ ({axis cs:0,0}) - (\p2) $),                         \n1={\x3/\x1}                     in                         (\p2) -- +($ {\n1}*(\x1,\y1) $) %                            node [Point,fill=Tangent] (origin intersection) {} %                            node [Point,fill=Curve] at (left intersection-1) {}                     ; %                    % ---------- %                    % draw the horizontal line at the curve intersection point %                    % plus the label above/below the line %                    \tikzmath{ %                        coordinate \c1; %                        \c1=(left intersection-1) - (right intersection-1); %                        \slope=\cy1/\cx1*sign(#1); %                    } %                    \pgfmathsetmacro{\AboveBelow}{ \slope>0 ? "above" : "below" } %                    \draw [dotted] %                        ([xshift=sign(#1)*2.5mm] left intersection-1) -- %                        (left intersection-1) -- %                            node [\AboveBelow,node font=\scriptsize] {$f(x)$} %                        (left intersection-1 -| origin intersection) -- %                        +($ sign(#1)*(-2.5mm,0) $) %                            coordinate [pos=0.5] (a) %                    ; %                    % draw the horizontal line at the ordinate intersection point %                    \draw [dotted] (origin intersection) %                        +($ sign(#1)*(-2.5mm,0) $) -- %                        (origin intersection); %                    % draw vertical line left/right of the ordinate %                    \pgfmathsetmacro{\LeftRight}{ #1<0 ? "right" : "left" } %                    \draw [stealth-stealth] (origin intersection) %                        +($ sign(#1)*(-1.25mm,0) $) -- (a) %                            node [midway,\LeftRight,node font=\scriptsize] {$p$} %                    ; %                    % ---------------------------------------------------------                         \endgroup                 },             },         }     \makeatother \begin{document}     \begin{tikzpicture}         \begin{axis}[             axis lines=middle,             enlargelimits=0.1,             xmin=-0.5,             xmax=3.25,             ymin=0,             ymax=5.5,             xtick=\empty,             ytick=\empty,             xlabel=$x$,             ylabel=$y$,             domain=\pgfkeysvalueof{/pgfplots/xmin}:(\pgfkeysvalueof{/pgfplots/xmax},             samples=50,             tangent/.style={                 add node at x={#1}{},             },         ]             \addplot [thick,draw=Curve,                 tangent=-0.5,                 tangent=0.8,                 tangent=2.3,             ] {0.5*x^2 - 2*x + 4};         \end{axis}     \end{tikzpicture} \end{document}                  

The above code results in

and when you uncomment the commented lines you will get

How To Draw A Tangent To A Curve

Source: https://tex.stackexchange.com/questions/290241/how-to-draw-a-tangent-line-to-an-arbitrary-addplot

Posted by: jacobsfooster.blogspot.com

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