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

Question

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?

Duplicate: https://mathematica.stackexchange.com/questions/87375/plotting-the-tangent-of-a-curve, which is a duplicate of https://mathematica.stackexchange.com/questions/18090/sliding-a-tangent-line-along-a-curve — Michael E2, Feb 25 '19 at 04:38

kglr · Accepted Answer · 2019-02-24T07:11:41.057

6

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]]]

edited Feb 24 '19 at 07:11

answered Feb 24 '19 at 06:05

kglr

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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 '19 at 06:50
@Jaigus, there was a typo; fixed now. Mesh -> {{1/2}} should be Mesh -> {{x0}}. – kglr Feb 24 '19 at 07:12
Thanks alot, this works great. – Jaigus Feb 24 '19 at 07:25
1

Alternatively: Plot[{function[x], Normal[Series[function[x], {x, x0, 1}]]} // Evaluate, {x, -5, 5}]. – J. M.'s missing motivation Feb 25 '19 at 02:04
@J.M.iscomputer-less, that's much neater. – kglr Feb 25 '19 at 07:04

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

1 Answers1