Examples for

Cusps & Corners

Cusps and corners are points on the curve defined by a continuous function that are singular points or where the derivative of the function does not exist. A cusp, or spinode, is a point where two branches of the curve meet and the tangents of each branch are equal. A corner is, more generally, any point where a continuous function's derivative is discontinuous. Use Wolfram|Alpha to locate and visualize cusps and corners.


Discover cusp points of functions.

Find cusps on the graph of a function:


Explore corner points of mathematical expressions.

Find corners on the graph of a function: