What is Cusp and what are the values of derivatives

[Ali Asadullah]

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

 

[Gib Z]

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.