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.
Cusps

Discover cusp points of functions.

Find cusps on the graph of a function:

cusps of sqrt |x-2| - cbrt |x+2|
cusps 1+x-(x^2(1-sqrt(7)x^2)^2)^(1/3)
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Corners

Explore corner points of mathematical expressions.

Find corners on the graph of a function:

corners of x + 2 |sin x|
corners |x^3 - 2x^2 - 16x + 6|
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