## What does a cusp look like?

### In mathematics, a cusp refers to a point on a curve where the curve has a sharp corner or bends suddenly

In mathematics, a cusp refers to a point on a curve where the curve has a sharp corner or bends suddenly. The shape of a cusp can vary depending on the type of curve.

For example, in a simple case, consider the curve of the graph of the function y = x^3. This curve has a cusp at the origin (0,0). As you approach the origin from the left side of the graph, the curve sharply bends upwards, creating a pointed corner. Similarly, as you approach the origin from the right side, the curve sharply bends downwards, again creating a pointed corner. The point where these two branches meet is the cusp.

In general, a cusp is characterized by having a sharp, pointed tip where the curve changes direction abruptly. The shape of the cusp can differ depending on the specific equation or function defining the curve.

Cusps can also appear in other mathematical contexts, such as in the study of parametric curves or in differential geometry. In these cases, cusps still exhibit the same characteristic of abrupt change in direction or curvature.

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