How do I label critical points on the plot of a curve?

Clash Royale CLAN TAG#URR8PPP

up vote
1
down vote

favorite

1

I want to label the local maxima, local minima, and points of inflection on a plot of a curve. How is this done in Mathematica?

plotting calculus-and-analysis

share

edited 1 hour ago

m_goldberg

82.7k870190

asked 2 hours ago

Saurabh Patel

61

New contributor

Saurabh Patel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  Have you tried anything? Do you have an example function?
  – J. M. is somewhat okay.♦
  2 hours ago
  

  
  
  
  

add a comment | 

up vote
1
down vote

favorite

1

I want to label the local maxima, local minima, and points of inflection on a plot of a curve. How is this done in Mathematica?

plotting calculus-and-analysis

share

edited 1 hour ago

m_goldberg

82.7k870190

asked 2 hours ago

Saurabh Patel

61

New contributor

Saurabh Patel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  Have you tried anything? Do you have an example function?
  – J. M. is somewhat okay.♦
  2 hours ago
  

  
  
  
  

add a comment | 

up vote
1
down vote

favorite

1

up vote
1
down vote

favorite

1

1

I want to label the local maxima, local minima, and points of inflection on a plot of a curve. How is this done in Mathematica?

plotting calculus-and-analysis

share

edited 1 hour ago

m_goldberg

82.7k870190

asked 2 hours ago

Saurabh Patel

61

New contributor

Saurabh Patel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

I want to label the local maxima, local minima, and points of inflection on a plot of a curve. How is this done in Mathematica?

plotting calculus-and-analysis

plotting calculus-and-analysis

share

edited 1 hour ago

m_goldberg

82.7k870190

asked 2 hours ago

Saurabh Patel

61

New contributor

Saurabh Patel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share

edited 1 hour ago

m_goldberg

82.7k870190

asked 2 hours ago

Saurabh Patel

61

New contributor

Saurabh Patel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share

share

edited 1 hour ago

m_goldberg

82.7k870190

edited 1 hour ago

m_goldberg

82.7k870190

edited 1 hour ago

m_goldberg

82.7k870190

82.7k870190

asked 2 hours ago

Saurabh Patel

61

New contributor

Saurabh Patel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 2 hours ago

Saurabh Patel

61

asked 2 hours ago

Saurabh Patel

61

61

New contributor

Saurabh Patel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

New contributor

Saurabh Patel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

Saurabh Patel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  Have you tried anything? Do you have an example function?
  – J. M. is somewhat okay.♦
  2 hours ago
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  Have you tried anything? Do you have an example function?
  – J. M. is somewhat okay.♦
  2 hours ago
  

  
  
  
  

3

3

Have you tried anything? Do you have an example function?
– J. M. is somewhat okay.♦
2 hours ago

Have you tried anything? Do you have an example function?
– J. M. is somewhat okay.♦
2 hours ago

add a comment | 

1 Answer
1

active

oldest

votes

up vote
3
down vote

One way to produce such labeling as you ask for is to use Callout. However, Callout only works in plots and not in graphic directives. This complicates things a little because Epilog can't be used to show the points. I resort to plotting the curve on one plot and the critical points and their labels on another and then combining the two with Show.

Here is an example using a cubic polynomial as the curve.

f[x_] := x (x - 1) (x + 1)

pts = #, f[#] & /@ -(1/Sqrt[3]), 0, 1/Sqrt[3] // Nl;
lbls = "max", "inflection", "min";
places = Automatic, Automatic, .63, -.43;

pts are the critical points
lbls are their labels
places are where they will be placed. Note that I only override Mathematica's automatic placement for the minimum. I was OK with the placement of the other two points.

With[max = 1,
 curve = Plot[f[x], x, -max, max];
 points = 
 ListPlot[MapThread[Callout[#1, #2, #3] &, pts, lbls, places],
 PlotRange -> -max, max, Automatic,
 PlotStyle -> Red, AbsolutePointSize[8]]];

Show[curve, points, PlotRange -> All]

share|improve this answer

answered 42 mins ago

m_goldberg

82.7k870190

add a comment | 

Your Answer

StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "387"
;
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',
convertImagesToLinks: false,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);

Saurabh Patel is a new contributor. Be nice, and check out our Code of Conduct.

 

draft saved

draft discarded

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

Name Email

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f183510%2fhow-do-i-label-critical-points-on-the-plot-of-a-curve%23new-answer', 'question_page');

);

Post as a guest

Name Email

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
3
down vote

One way to produce such labeling as you ask for is to use Callout. However, Callout only works in plots and not in graphic directives. This complicates things a little because Epilog can't be used to show the points. I resort to plotting the curve on one plot and the critical points and their labels on another and then combining the two with Show.

Here is an example using a cubic polynomial as the curve.

f[x_] := x (x - 1) (x + 1)

pts = #, f[#] & /@ -(1/Sqrt[3]), 0, 1/Sqrt[3] // Nl;
lbls = "max", "inflection", "min";
places = Automatic, Automatic, .63, -.43;

pts are the critical points
lbls are their labels
places are where they will be placed. Note that I only override Mathematica's automatic placement for the minimum. I was OK with the placement of the other two points.

With[max = 1,
 curve = Plot[f[x], x, -max, max];
 points = 
 ListPlot[MapThread[Callout[#1, #2, #3] &, pts, lbls, places],
 PlotRange -> -max, max, Automatic,
 PlotStyle -> Red, AbsolutePointSize[8]]];

Show[curve, points, PlotRange -> All]

share|improve this answer

answered 42 mins ago

m_goldberg

82.7k870190

add a comment | 

up vote
3
down vote

One way to produce such labeling as you ask for is to use Callout. However, Callout only works in plots and not in graphic directives. This complicates things a little because Epilog can't be used to show the points. I resort to plotting the curve on one plot and the critical points and their labels on another and then combining the two with Show.

Here is an example using a cubic polynomial as the curve.

f[x_] := x (x - 1) (x + 1)

pts = #, f[#] & /@ -(1/Sqrt[3]), 0, 1/Sqrt[3] // Nl;
lbls = "max", "inflection", "min";
places = Automatic, Automatic, .63, -.43;

pts are the critical points
lbls are their labels
places are where they will be placed. Note that I only override Mathematica's automatic placement for the minimum. I was OK with the placement of the other two points.

With[max = 1,
 curve = Plot[f[x], x, -max, max];
 points = 
 ListPlot[MapThread[Callout[#1, #2, #3] &, pts, lbls, places],
 PlotRange -> -max, max, Automatic,
 PlotStyle -> Red, AbsolutePointSize[8]]];

Show[curve, points, PlotRange -> All]

share|improve this answer

answered 42 mins ago

m_goldberg

82.7k870190

add a comment | 

up vote
3
down vote

up vote
3
down vote

One way to produce such labeling as you ask for is to use Callout. However, Callout only works in plots and not in graphic directives. This complicates things a little because Epilog can't be used to show the points. I resort to plotting the curve on one plot and the critical points and their labels on another and then combining the two with Show.

Here is an example using a cubic polynomial as the curve.

f[x_] := x (x - 1) (x + 1)

pts = #, f[#] & /@ -(1/Sqrt[3]), 0, 1/Sqrt[3] // Nl;
lbls = "max", "inflection", "min";
places = Automatic, Automatic, .63, -.43;

pts are the critical points
lbls are their labels
places are where they will be placed. Note that I only override Mathematica's automatic placement for the minimum. I was OK with the placement of the other two points.

With[max = 1,
 curve = Plot[f[x], x, -max, max];
 points = 
 ListPlot[MapThread[Callout[#1, #2, #3] &, pts, lbls, places],
 PlotRange -> -max, max, Automatic,
 PlotStyle -> Red, AbsolutePointSize[8]]];

Show[curve, points, PlotRange -> All]

share|improve this answer

answered 42 mins ago

m_goldberg

82.7k870190

One way to produce such labeling as you ask for is to use Callout. However, Callout only works in plots and not in graphic directives. This complicates things a little because Epilog can't be used to show the points. I resort to plotting the curve on one plot and the critical points and their labels on another and then combining the two with Show.

Here is an example using a cubic polynomial as the curve.

f[x_] := x (x - 1) (x + 1)

pts = #, f[#] & /@ -(1/Sqrt[3]), 0, 1/Sqrt[3] // Nl;
lbls = "max", "inflection", "min";
places = Automatic, Automatic, .63, -.43;

pts are the critical points
lbls are their labels
places are where they will be placed. Note that I only override Mathematica's automatic placement for the minimum. I was OK with the placement of the other two points.

With[max = 1,
 curve = Plot[f[x], x, -max, max];
 points = 
 ListPlot[MapThread[Callout[#1, #2, #3] &, pts, lbls, places],
 PlotRange -> -max, max, Automatic,
 PlotStyle -> Red, AbsolutePointSize[8]]];

Show[curve, points, PlotRange -> All]

share|improve this answer

answered 42 mins ago

m_goldberg

82.7k870190

share|improve this answer

share|improve this answer

answered 42 mins ago

m_goldberg

82.7k870190

answered 42 mins ago

m_goldberg

82.7k870190

answered 42 mins ago

m_goldberg

82.7k870190

82.7k870190

add a comment | 

add a comment | 

Saurabh Patel is a new contributor. Be nice, and check out our Code of Conduct.

 

draft saved

draft discarded

Saurabh Patel is a new contributor. Be nice, and check out our Code of Conduct.

Saurabh Patel is a new contributor. Be nice, and check out our Code of Conduct.

Saurabh Patel is a new contributor. Be nice, and check out our Code of Conduct.

 

draft saved

draft discarded

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

Name Email

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f183510%2fhow-do-i-label-critical-points-on-the-plot-of-a-curve%23new-answer', 'question_page');

);

Post as a guest

Name Email

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

Name Email

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

Name Email

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

Name Email

Name Email

Name

Email

Name Email

Name

Email