Intersection library and Differential approximations
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 {$$};%%Found by slope formula then trial and error
%%%
draw[dashed] (2.25,1.28125)--(3,1.28125);
draw[dashed] (3,2.125)--(3,1.28125);
draw[dashed] (2.9,1.28125)--(2.9,1.38125)--(3,1.38125);
%%%
draw[decoration={brace,raise=5pt},decorate,thick]
(4,2.125) -- node[right=6pt] {textcolor{blue}{$Delta y$}} (4,1.28125);
draw[dashed] (4,2.125)--(3,2.125);
draw[dashed] (4,1.28125)--(3,1.28125);
draw[decoration={brace,mirror,raise=5pt},decorate,thick]
(2.25,1.28125) -- node[below=6pt] {textcolor{blue}{$Delta x$}}
(3,1.28125);
draw[dashed] (2.25,1.28125)--(2.25,0);
node at (.75,1.75) {$y=f(x)$};
%%%
filldraw[black] (3,2.125) circle (1pt) node[left] {};
end{scope}
end{tikzpicture}
end{center}
end{document}
This outputs:
I would like tikz to calculate the point rather than an estimate.
tikz-pgf intersections
add a comment |
Hi everyone I am looking for a smoother program using the intersection library to calculate where the tangent line intersects the vertical line of the x-coordinate of the second coordinate. I have so far:
documentclass{article}
usepackage{tikz}
usepackage{geometry}
usetikzlibrary{decorations.pathreplacing}
usetikzlibrary{intersections}
begin{document}
newcommand*{DeltaX}{0.01}
newcommand*{DrawTangentLabel}[5]{%
% #1 = draw options
% #2 = name of curve
% #3 = ymin
% #4 = ymax
% #5 = x value at which tangent is to be drawn
path[name path=Vertical Line Left] (#5-DeltaX,#3) -- (#5-DeltaX,#4);
path[name path=Vertical Line Right] (#5+DeltaX,#3) -- (#5+DeltaX,#4);
path [name intersections={of=Vertical Line Left and #2}];
coordinate (X0) at (intersection-1);
path [name intersections={of=Vertical Line Right and #2}];
coordinate (X1) at (intersection-1);
draw [shorten <= -3cm, shorten >= -3cm, #1] (X0) -- (X1) node {$$};
}%
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.
tikz-pgf intersections
add a comment |
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 {$$};%%Found by slope formula then trial and error
%%%
draw[dashed] (2.25,1.28125)--(3,1.28125);
draw[dashed] (3,2.125)--(3,1.28125);
draw[dashed] (2.9,1.28125)--(2.9,1.38125)--(3,1.38125);
%%%
draw[decoration={brace,raise=5pt},decorate,thick]
(4,2.125) -- node[right=6pt] {textcolor{blue}{$Delta y$}} (4,1.28125);
draw[dashed] (4,2.125)--(3,2.125);
draw[dashed] (4,1.28125)--(3,1.28125);
draw[decoration={brace,mirror,raise=5pt},decorate,thick]
(2.25,1.28125) -- node[below=6pt] {textcolor{blue}{$Delta x$}}
(3,1.28125);
draw[dashed] (2.25,1.28125)--(2.25,0);
node at (.75,1.75) {$y=f(x)$};
%%%
filldraw[black] (3,2.125) circle (1pt) node[left] {};
end{scope}
end{tikzpicture}
end{center}
end{document}
This outputs:
I would like tikz to calculate the point rather than an estimate.
tikz-pgf intersections
Hi everyone I am looking for a smoother program using the intersection library to calculate where the tangent line intersects the vertical line of the x-coordinate of the second coordinate. I have so far:
documentclass{article}
usepackage{tikz}
usepackage{geometry}
usetikzlibrary{decorations.pathreplacing}
usetikzlibrary{intersections}
begin{document}
newcommand*{DeltaX}{0.01}
newcommand*{DrawTangentLabel}[5]{%
% #1 = draw options
% #2 = name of curve
% #3 = ymin
% #4 = ymax
% #5 = x value at which tangent is to be drawn
path[name path=Vertical Line Left] (#5-DeltaX,#3) -- (#5-DeltaX,#4);
path[name path=Vertical Line Right] (#5+DeltaX,#3) -- (#5+DeltaX,#4);
path [name intersections={of=Vertical Line Left and #2}];
coordinate (X0) at (intersection-1);
path [name intersections={of=Vertical Line Right and #2}];
coordinate (X1) at (intersection-1);
draw [shorten <= -3cm, shorten >= -3cm, #1] (X0) -- (X1) node {$$};
}%
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.
tikz-pgf intersections
tikz-pgf intersections
edited Jan 23 at 20:12
MathScholar
asked Jan 23 at 20:01
MathScholarMathScholar
94029
94029
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
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}
add a comment |
Your Answer
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "85"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2ftex.stackexchange.com%2fquestions%2f471557%2fintersection-library-and-differential-approximations%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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}
add a comment |
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}
add a comment |
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}
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}
edited Jan 23 at 20:39
answered Jan 23 at 20:32
Torbjørn T.Torbjørn T.
157k13252442
157k13252442
add a comment |
add a comment |
Thanks for contributing an answer to TeX - LaTeX Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2ftex.stackexchange.com%2fquestions%2f471557%2fintersection-library-and-differential-approximations%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown