How do I draw a function along with a particular tangent line at a specific point? [duplicate]

This question already has an answer here:

Equation of a line that is tangent to a curve at point

2 answers

I would like to draw a function (x/x^2+1), and at a certain point, i'd like to draw a dot along with the tangent line at that specific point.

what I have tried is the following:

Plot[function[x], function'[x], x, -5, 5, AxesLabel -> x, y LabelStyle -> Direction[Black, Bold]]

However, this plots the original function f(x) and f'(x) simultaneously; how can I achieve the desired result?

edited Feb 25 at 2:04

J. M. is slightly pensive♦

98.1k10306465

asked Feb 24 at 5:38

Jaigus

1775

marked as duplicate by J. M. is slightly pensive♦ plotting
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Mar 13 at 2:19

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

$begingroup$
Duplicate: mathematica.stackexchange.com/questions/87375/…, which is a duplicate of mathematica.stackexchange.com/questions/18090/…
$endgroup$
– Michael E2
Feb 25 at 4:38

$begingroup$
Also this thread.
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 7:06

add a comment |

This question already has an answer here:

Equation of a line that is tangent to a curve at point

2 answers

I would like to draw a function (x/x^2+1), and at a certain point, i'd like to draw a dot along with the tangent line at that specific point.

what I have tried is the following:

Plot[function[x], function'[x], x, -5, 5, AxesLabel -> x, y LabelStyle -> Direction[Black, Bold]]

However, this plots the original function f(x) and f'(x) simultaneously; how can I achieve the desired result?

edited Feb 25 at 2:04

J. M. is slightly pensive♦

98.1k10306465

asked Feb 24 at 5:38

Jaigus

1775

marked as duplicate by J. M. is slightly pensive♦ plotting
Users with the plotting badge can single-handedly close plotting questions as duplicates and reopen them as needed.

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Mar 13 at 2:19

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

$begingroup$
Duplicate: mathematica.stackexchange.com/questions/87375/…, which is a duplicate of mathematica.stackexchange.com/questions/18090/…
$endgroup$
– Michael E2
Feb 25 at 4:38

$begingroup$
Also this thread.
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 7:06

add a comment |

This question already has an answer here:

Equation of a line that is tangent to a curve at point

2 answers

I would like to draw a function (x/x^2+1), and at a certain point, i'd like to draw a dot along with the tangent line at that specific point.

what I have tried is the following:

Plot[function[x], function'[x], x, -5, 5, AxesLabel -> x, y LabelStyle -> Direction[Black, Bold]]

However, this plots the original function f(x) and f'(x) simultaneously; how can I achieve the desired result?

edited Feb 25 at 2:04

J. M. is slightly pensive♦

98.1k10306465

asked Feb 24 at 5:38

Jaigus

1775

This question already has an answer here:

Equation of a line that is tangent to a curve at point

2 answers

I would like to draw a function (x/x^2+1), and at a certain point, i'd like to draw a dot along with the tangent line at that specific point.

what I have tried is the following:

Plot[function[x], function'[x], x, -5, 5, AxesLabel -> x, y LabelStyle -> Direction[Black, Bold]]

However, this plots the original function f(x) and f'(x) simultaneously; how can I achieve the desired result?

This question already has an answer here:

Equation of a line that is tangent to a curve at point

2 answers

plotting calculus-and-analysis functions

edited Feb 25 at 2:04

J. M. is slightly pensive♦

98.1k10306465

asked Feb 24 at 5:38

Jaigus

1775

edited Feb 25 at 2:04

J. M. is slightly pensive♦

98.1k10306465

asked Feb 24 at 5:38

Jaigus

1775

edited Feb 25 at 2:04

J. M. is slightly pensive♦

98.1k10306465

edited Feb 25 at 2:04

J. M. is slightly pensive♦

98.1k10306465

edited Feb 25 at 2:04

J. M. is slightly pensive♦

98.1k10306465

asked Feb 24 at 5:38

Jaigus

1775

asked Feb 24 at 5:38

Jaigus

1775

asked Feb 24 at 5:38

Jaigus

1775

marked as duplicate by J. M. is slightly pensive♦ plotting
Users with the plotting badge can single-handedly close plotting questions as duplicates and reopen them as needed.

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Mar 13 at 2:19

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

marked as duplicate by J. M. is slightly pensive♦ plotting
Users with the plotting badge can single-handedly close plotting questions as duplicates and reopen them as needed.

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Mar 13 at 2:19

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

$begingroup$
Duplicate: mathematica.stackexchange.com/questions/87375/…, which is a duplicate of mathematica.stackexchange.com/questions/18090/…
$endgroup$
– Michael E2
Feb 25 at 4:38

$begingroup$
Also this thread.
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 7:06

add a comment |

$begingroup$
Duplicate: mathematica.stackexchange.com/questions/87375/…, which is a duplicate of mathematica.stackexchange.com/questions/18090/…
$endgroup$
– Michael E2
Feb 25 at 4:38

$begingroup$
Also this thread.
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 7:06

Duplicate: mathematica.stackexchange.com/questions/87375/…, which is a duplicate of mathematica.stackexchange.com/questions/18090/…

– Michael E2
Feb 25 at 4:38

Also this thread.

– J. M. is slightly pensive♦
Feb 25 at 7:06

add a comment |

1 Answer
1

active

oldest

votes

function[x_] := x/(x^2 + 1);

x0 = 1/2; 
Plot[function[x], function[x0] + function'[x0] (x - x0), x, -5, 5, 
 AxesLabel -> x, y, LabelStyle -> Direction[Black, Bold], 
 Mesh -> x0, MeshStyle -> Directive[Red, PointSize[Large]]]

enter image description here

edited Feb 24 at 7:11

answered Feb 24 at 6:05

kglr

189k10206424

$begingroup$
Hey thanks! I'm trying to plot this at point 45, but it doesn't seem to plot the tangent at that point; instead the tangent is on a completely different line with two dots?
$endgroup$
– Jaigus
Feb 24 at 6:50

$begingroup$
@Jaigus, there was a typo; fixed now. Mesh -> 1/2 should be Mesh -> x0.
$endgroup$
– kglr
Feb 24 at 7:12

$begingroup$
Thanks alot, this works great.
$endgroup$
– Jaigus
Feb 24 at 7:25

1

$begingroup$
Alternatively: Plot[function[x], Normal[Series[function[x], x, x0, 1]] // Evaluate, x, -5, 5].
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 2:04

$begingroup$
@J.M.iscomputer-less, that's much neater.
$endgroup$
– kglr
Feb 25 at 7:04

add a comment |

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

function[x_] := x/(x^2 + 1);

x0 = 1/2; 
Plot[function[x], function[x0] + function'[x0] (x - x0), x, -5, 5, 
 AxesLabel -> x, y, LabelStyle -> Direction[Black, Bold], 
 Mesh -> x0, MeshStyle -> Directive[Red, PointSize[Large]]]

enter image description here

edited Feb 24 at 7:11

answered Feb 24 at 6:05

kglr

189k10206424

$begingroup$
Hey thanks! I'm trying to plot this at point 45, but it doesn't seem to plot the tangent at that point; instead the tangent is on a completely different line with two dots?
$endgroup$
– Jaigus
Feb 24 at 6:50

$begingroup$
@Jaigus, there was a typo; fixed now. Mesh -> 1/2 should be Mesh -> x0.
$endgroup$
– kglr
Feb 24 at 7:12

$begingroup$
Thanks alot, this works great.
$endgroup$
– Jaigus
Feb 24 at 7:25

1

$begingroup$
Alternatively: Plot[function[x], Normal[Series[function[x], x, x0, 1]] // Evaluate, x, -5, 5].
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 2:04

$begingroup$
@J.M.iscomputer-less, that's much neater.
$endgroup$
– kglr
Feb 25 at 7:04

add a comment |

function[x_] := x/(x^2 + 1);

x0 = 1/2; 
Plot[function[x], function[x0] + function'[x0] (x - x0), x, -5, 5, 
 AxesLabel -> x, y, LabelStyle -> Direction[Black, Bold], 
 Mesh -> x0, MeshStyle -> Directive[Red, PointSize[Large]]]

enter image description here

edited Feb 24 at 7:11

answered Feb 24 at 6:05

kglr

189k10206424

$begingroup$
Hey thanks! I'm trying to plot this at point 45, but it doesn't seem to plot the tangent at that point; instead the tangent is on a completely different line with two dots?
$endgroup$
– Jaigus
Feb 24 at 6:50

$begingroup$
@Jaigus, there was a typo; fixed now. Mesh -> 1/2 should be Mesh -> x0.
$endgroup$
– kglr
Feb 24 at 7:12

$begingroup$
Thanks alot, this works great.
$endgroup$
– Jaigus
Feb 24 at 7:25

1

$begingroup$
Alternatively: Plot[function[x], Normal[Series[function[x], x, x0, 1]] // Evaluate, x, -5, 5].
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 2:04

$begingroup$
@J.M.iscomputer-less, that's much neater.
$endgroup$
– kglr
Feb 25 at 7:04

add a comment |

function[x_] := x/(x^2 + 1);

x0 = 1/2; 
Plot[function[x], function[x0] + function'[x0] (x - x0), x, -5, 5, 
 AxesLabel -> x, y, LabelStyle -> Direction[Black, Bold], 
 Mesh -> x0, MeshStyle -> Directive[Red, PointSize[Large]]]

enter image description here

edited Feb 24 at 7:11

answered Feb 24 at 6:05

kglr

189k10206424

function[x_] := x/(x^2 + 1);

x0 = 1/2; 
Plot[function[x], function[x0] + function'[x0] (x - x0), x, -5, 5, 
 AxesLabel -> x, y, LabelStyle -> Direction[Black, Bold], 
 Mesh -> x0, MeshStyle -> Directive[Red, PointSize[Large]]]

enter image description here

edited Feb 24 at 7:11

answered Feb 24 at 6:05

kglr

189k10206424

edited Feb 24 at 7:11

answered Feb 24 at 6:05

kglr

189k10206424

answered Feb 24 at 6:05

kglr

189k10206424

answered Feb 24 at 6:05

kglr

189k10206424

$begingroup$
Hey thanks! I'm trying to plot this at point 45, but it doesn't seem to plot the tangent at that point; instead the tangent is on a completely different line with two dots?
$endgroup$
– Jaigus
Feb 24 at 6:50

$begingroup$
@Jaigus, there was a typo; fixed now. Mesh -> 1/2 should be Mesh -> x0.
$endgroup$
– kglr
Feb 24 at 7:12

$begingroup$
Thanks alot, this works great.
$endgroup$
– Jaigus
Feb 24 at 7:25

1

$begingroup$
Alternatively: Plot[function[x], Normal[Series[function[x], x, x0, 1]] // Evaluate, x, -5, 5].
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 2:04

$begingroup$
@J.M.iscomputer-less, that's much neater.
$endgroup$
– kglr
Feb 25 at 7:04

add a comment |

$begingroup$
Hey thanks! I'm trying to plot this at point 45, but it doesn't seem to plot the tangent at that point; instead the tangent is on a completely different line with two dots?
$endgroup$
– Jaigus
Feb 24 at 6:50

$begingroup$
@Jaigus, there was a typo; fixed now. Mesh -> 1/2 should be Mesh -> x0.
$endgroup$
– kglr
Feb 24 at 7:12

$begingroup$
Thanks alot, this works great.
$endgroup$
– Jaigus
Feb 24 at 7:25

1

$begingroup$
Alternatively: Plot[function[x], Normal[Series[function[x], x, x0, 1]] // Evaluate, x, -5, 5].
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 2:04

$begingroup$
@J.M.iscomputer-less, that's much neater.
$endgroup$
– kglr
Feb 25 at 7:04

Hey thanks! I'm trying to plot this at point 45, but it doesn't seem to plot the tangent at that point; instead the tangent is on a completely different line with two dots?

– Jaigus
Feb 24 at 6:50

@Jaigus, there was a typo; fixed now. Mesh -> 1/2 should be Mesh -> x0.

– kglr
Feb 24 at 7:12

Thanks alot, this works great.

– Jaigus
Feb 24 at 7:25

Alternatively: Plot[function[x], Normal[Series[function[x], x, x0, 1]] // Evaluate, x, -5, 5].

– J. M. is slightly pensive♦
Feb 25 at 2:04

@J.M.iscomputer-less, that's much neater.

– kglr
Feb 25 at 7:04

add a comment |

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