# What is Cusp and what are the values of derivatives

1. Feb 12, 2010

What is Cusp and what are the values of derivatives on left and right side of it?

2. Feb 12, 2010

### Gib Z

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; $x^3-y^2=0$, which has a cusp at the origin. We see this as the two branches of the curve, $$y=x^{\frac{3}{2}}$$ and $$y=-x^{\frac{3}{2}}$$ both have the limiting tangent y=0.