Xrhrft

Hi everyone I am looking for a smoother program using the intersection library to calculate where the tangent line intersects the vertical line of the x-coordinate of the second coordinate. I have so far:

documentclass{article}

usepackage{tikz}

usepackage{geometry}

usetikzlibrary{decorations.pathreplacing}

usetikzlibrary{intersections}



begin{document}



newcommand*{DeltaX}{0.01}

newcommand*{DrawTangentLabel}[5]{%

 % #1 = draw options

 % #2 = name of curve

 % #3 = ymin

 % #4 = ymax

 % #5 = x value at which tangent is to be drawn



path[name path=Vertical Line Left]  (#5-DeltaX,#3) -- (#5-DeltaX,#4);

path[name path=Vertical Line Right] (#5+DeltaX,#3) -- (#5+DeltaX,#4);



path [name intersections={of=Vertical Line Left and #2}];

coordinate (X0) at (intersection-1);

path [name intersections={of=Vertical Line Right and #2}];

coordinate (X1) at (intersection-1);



draw [shorten <= -3cm, shorten >= -3cm, #1] (X0) -- (X1)  node {$$};

}%



begin{center}

begin{tikzpicture}[scale=1.75,cap=round]

  tikzset{axes/.style={}}

%draw[style=help lines,step=1cm, dotted] (-5.25,-5.25) grid (5.25,5.25);

% The graphic

begin{scope}[style=axes]

draw[->] (-.5,0) -- (4.5,0) node[below] {$x$};

draw[->] (0,-.5)-- (0,3) node[left] {$y$};

foreach x/xtext in {2.25/x}

 draw[xshift=x cm] (0pt,2pt) -- (0pt,-2pt)  

     node[below,fill=white,font=normalsize]

  {$xtext$};    

  %%%

  draw[name path=curve, domain=.5:3.25,smooth,variable=x,black,<->,thick] 

  plot ({x},{.5*(x-1.5)*(x-1.5)+1});

 DrawTangentLabel[red,thick,<->]{curve}{-1}{3}{2.25}

 draw[name path=curve, domain=.5:3.25,smooth,variable=x,black,<->,thick] plot ({x},{.5*(x-1.5)*(x-1.5)+1});

  %%%

 filldraw[black] (2.25,1.28125) circle (1pt) node {$$};

 filldraw[black] (3,1.28125) circle (1pt) node {$$};

 filldraw[black] (3,2.125) circle (1pt) node {$$};

 filldraw[black] (3,1.775) circle (1pt) node {$$};%%Found by slope formula then trial and error

  %%%

  draw[dashed] (2.25,1.28125)--(3,1.28125); 

  draw[dashed] (3,2.125)--(3,1.28125);

  draw[dashed] (2.9,1.28125)--(2.9,1.38125)--(3,1.38125);

  %%%

  draw[decoration={brace,raise=5pt},decorate,thick]

   (4,2.125) -- node[right=6pt] {textcolor{blue}{$Delta y$}} (4,1.28125);

 draw[dashed] (4,2.125)--(3,2.125);

 draw[dashed] (4,1.28125)--(3,1.28125);    

 draw[decoration={brace,mirror,raise=5pt},decorate,thick]

   (2.25,1.28125) -- node[below=6pt] {textcolor{blue}{$Delta x$}} 

  (3,1.28125);

 draw[dashed]  (2.25,1.28125)--(2.25,0);

 node at (.75,1.75)  {$y=f(x)$};

%%%

 filldraw[black] (3,2.125) circle (1pt) node[left] {};

 end{scope}

 end{tikzpicture}

 end{center}



end{document}

This outputs:

I would like tikz to calculate the point rather than an estimate.

If you instead of shorten use the syntax of the calc library to draw the tangent line, you can use the intersections library to find the intersection.

documentclass{article}

usepackage{tikz}

usetikzlibrary{decorations.pathreplacing}

usetikzlibrary{calc} % <-- added

usetikzlibrary{intersections}



begin{document}



newcommand*{DeltaX}{0.01}

newcommand*{DrawTangentLabel}[5]{%

 % #1 = draw options

 % #2 = name of curve

 % #3 = ymin

 % #4 = ymax

 % #5 = x value at which tangent is to be drawn



path[name path=Vertical Line Left]  (#5-DeltaX,#3) -- (#5-DeltaX,#4);

path[name path=Vertical Line Right] (#5+DeltaX,#3) -- (#5+DeltaX,#4);



path [name intersections={of=Vertical Line Left and #2}];

coordinate (X0) at (intersection-1);

path [name intersections={of=Vertical Line Right and #2}];

coordinate (X1) at (intersection-1);



draw [#1] ($(X0)!-2cm!(X1)$) -- ($(X1)!-2cm!(X0)$); % <-- modified

}%



begin{center}

begin{tikzpicture}[

   scale=1.75,

   cap=round,

   axes/.style={->},

   declare function={f(x)=.5*(x-1.5)*(x-1.5)+1;} % <-- added

]

%draw[style=help lines,step=1cm, dotted] (-5.25,-5.25) grid (5.25,5.25);

% The graphic



draw[axes] (-.5,0) -- (4.5,0) node[below] {$x$};

draw[axes] (0,-.5)-- (0,3) node[left] {$y$};



foreach x/xtext in {2.25/x}

  draw (x,2pt) -- (x,-2pt) node[below,fill=white,font=normalsize] {$xtext$};    





draw[name path=curve, domain=.5:3.25,smooth,<->,thick]   plot ({x},{f(x)});



DrawTangentLabel[red,thick,<->, name path=tangent]{curve}{-1}{3}{2.25}



foreach [count=i] x in {2.25,3}

    filldraw (x,{f(x)}) circle[radius=1pt] coordinate(ni);



draw [dashed,name path=dash] (n1) -| coordinate (n3) (n2);

filldraw (n3) circle[radius=1pt];



fill[name intersections={of=dash and tangent}] (intersection-1) circle[radius=1pt];





draw[decoration={brace,raise=5pt},decorate,thick] (n2 -| 4,0) -- node[right=6pt,blue] {$Delta y$} (n3 -| 4,0);

draw[decoration={brace,mirror,raise=5pt},decorate,thick]   (n1) -- node[below=6pt,blue] {$Delta x$} (n3);



draw[dashed] (n1) -- (n1 |- 0,0)

              (n2) -- (n2 -| 4,0)

              (n3) -- (n3 -| 4,0);



node [above]at (.5,{f(.5)}) {$y=f(x)$};

%%%



end{tikzpicture}

end{center}



end{document}