Curve sketching

It consists of plotting (α, β) for each term Axαyβ in the equation of the curve.

The resulting diagram is then analyzed to produce information about the curve.

Therefore, the significant terms near the origin under this assumption are only those lying on the line and the others may be ignored; it produces a simple approximate equation for the curve.

For example, the folium of Descartes is defined by the equation Then Newton's diagram has points at (3, 0), (1, 1), and (0, 3).

These produce as approximate equations for the horizontal and vertical branches of the curve where they cross at the origin.

Graph of the function 3 x 3 -5 x 2 +8 (black) and its first (9 x 2 -10 x , red) and second (18 x -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.