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What is Cusp and what are the values of derivatives

  1. Feb 12, 2010 #1
    What is Cusp and what are the values of derivatives on left and right side of it?
     
  2. jcsd
  3. Feb 12, 2010 #2

    Gib Z

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    Homework Helper

    Re: Cusp

    A Cusp is a point at which two branches of a curve meet such that the branches share a limiting tangent.

    A Cusp is a type of singular point on a curve (a point on a curve that does not have a defined derivative), and is considered "local" as it not a result of self intersections of the curve.

    The classic example of a cusp is the semicubical parabola; [itex]x^3-y^2=0[/itex], which has a cusp at the origin. We see this as the two branches of the curve, [tex]y=x^{\frac{3}{2}}[/tex] and [tex]y=-x^{\frac{3}{2}}[/tex] both have the limiting tangent y=0.
     
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