Curve sketching

Graph of the function 3x3-5x2+8 (black) and its first (9x2-10x, red) and second (18x-10, blue) derivatives. An x value where the y value of the red, or the blue, curve vanishes (becomes 0) gives rise to a local extremum (marked "HP", "TP"), or an inflection point ("WP"), of the black curve, respectively.

In geometry, curve sketching (or curve tracing) are techniques for producing a rough idea of overall shape of a plane curve given its equation, without computing the large numbers of points required for a detailed plot. It is an application of the theory of curves to find their main features.


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