cusp math definition

cusp math definition - A simple cusp is a point on a curve where the curve crosses itself, and where the two branches of the curve share a common tangent, the branches being on opposite sides of the tangent.

Basically its the point on the curve that turns back on itself. It looks symmetrical and the point on the curve where the branches meet share a common tangent point. This would be where the red point is on the graph below. The branches are also on opposite sides of the tangent.

For example, this plot shows the curve of y²=x³ which is a semicubical parabola.

Sometimes they are also called vertical cusps because they look like it is going double back on itself. In this case the graph is infinite. However, not all graphs are infinite that show signs of a cusp.

This is a not a cusp

Related words: Tangent, plot, graph, semi

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