A cusp is a point at which two branches of a curve meet such that the tangents of each branch are equal. The above plot shows the semicubical parabola curve , which has a cusp at the origin.

Walker, R. J. Algebraic Curves. New York: Springer-Verlag, pp. 57-58, 1978.

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Weisstein, Eric W. "Cusp." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Cusp.html