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TangentPlane (1.0.1) current version: 2.0.0 »

Source Notebook

Find the tangent plane of a function at a point

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["TangentPlane"][expr,{x,a},{y,b},z]

gives an association of properties of the tangent plane to expr, viewed as an equation in x,y and z, at the point x=a,y=b.

ResourceFunction["TangentPlane"][expr,{x,a},{y,b},z,prop]

returns the value of the tangent plane property prop.

Details

Allowed values of prop are "StandardFormEquation", "Slopes" and "Plot".

If expr does not have head Equal, then expr is treated as an expression defining z in terms of x and y or w in terms of x, y and z. In other words, ResourceFunction["TangentPlane"][expr,{x,a},y,…] is equivalent to ResourceFunction["TangentPlane"][z==expr,{x,a},{y,b},…] if expr itself has a head other than Equal.

Examples

Basic Examples (4)

Return the equation of the tangent plane to a surface:

In[1]:=

$ResourceFunction["TangentPlane"][ x^2 + y^2, {x, 2}, {y, 3}, z, "StandardFormEquation"]$

Out[1]=

Visualize the tangent plane:

In[2]:=

$ResourceFunction["TangentPlane"][x^2 + y^2, {x, 2}, {y, 3}, z, "Plot"]$

Out[2]=

Compute the slopes with respect to x and y:

In[3]:=

$ResourceFunction["TangentPlane"][ x^2 + y^2, {x, 2}, {y, 3}, z, "Slopes"]$

Out[3]=

Get an association of properties of a tangent plane to a surface:

In[4]:=

$ResourceFunction["TangentPlane"][x^2 + y^2, {x, 2}, {y, 3}, z]$

Out[4]=

Scope (2)

The first argument to TangentPlane can be an implicit definition of a surface:

In[5]:=

$ResourceFunction["TangentPlane"][ x^2 + y^2 + z^2 == 9, {x, 0}, {y, 0}, {z, -3}, "Plot"]$

Out[5]=

TangentPlane also works in four dimensions:

In[6]:=

$ResourceFunction["TangentPlane"][ w == x^2 + y^2 + z^2, {x, 2}, {y, 3}, {z, 5}, w, "StandardFormEquation"]$

Out[6]=

Version History

2.0.0 – 23 March 2023
1.1.0 – 25 March 2022
1.0.1 – 04 March 2021
1.0.0 – 20 March 2020

Related Resources

Author Notes

To view the full source code for TangentPlane, evaluate the following:

In[1]:=

License Information

This work is licensed under a Creative Commons Attribution 4.0 International License