Function Repository Resource:

FunctionCusps

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.

Compute the cusps of a curve:

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

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$Plot[x^(2/3), {x, -1, 1}]$

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In comparison with:

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$Plot[Surd[x^2, 3], {x, -1, 1}]$

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

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