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 FunctionCusps (2.0.0) current version: 3.0.0 »

Source Notebook

Find the cusps of a curve

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["FunctionCusps"][c,x]

returns the cusps of the curve c viewed as a function of x.

Details and Options

A cusp, or spinode, is a point where two branchs of a curve meet and the tangents of each branch are equal.

Examples

Basic Examples (1) 

Compute the cusps of a curve:

In[1]:=
ResourceFunction["FunctionCusps"][ArcTan[Log[Abs[x]]], x]
Out[1]=

Possible Issues (2) 

Note that when using fractional powers to define the expression, Surd may be necessary to extend the real-valued domain of the curve:

In[2]:=
ResourceFunction["FunctionCusps"][x^(2/3), x]
Out[2]=
In[3]:=
Plot[x^(2/3), {x, -1, 1}]
Out[3]=

In comparison with:

In[4]:=
ResourceFunction["FunctionCusps"][Surd[x^2, 3], x]
Out[4]=
In[5]:=
Plot[Surd[x^2, 3], {x, -1, 1}]
Out[5]=

Note the distinction between cusps and corners, which can be computed using the resource function FunctionCorners:

In[6]:=
ResourceFunction["FunctionCusps"][Abs[x], x]
Out[6]=
In[7]:=
ResourceFunction["FunctionCorners"][Abs[x], x]
Out[7]=

Publisher

Wolfram|Alpha Math Team

Version History

  • 3.0.0 – 23 March 2023
  • 2.0.0 – 08 April 2020
  • 1.0.0 – 06 April 2020

Related Resources

License Information