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2. Implicit curve - Wikipedia

   en.wikipedia.org/wiki/Implicit_curve

   Plane curves can be represented in Cartesian coordinates (x, y coordinates) by any of three methods, one of which is the implicit equation given above. The graph of a function is usually described by an equation = in which the functional form is explicitly stated; this is called an explicit representation.

3. Slope field - Wikipedia

   en.wikipedia.org/wiki/Slope_field

   The slope field can be defined for the following type of differential equations y ′ = f ( x , y ) , {\displaystyle y'=f(x,y),} which can be interpreted geometrically as giving the slope of the tangent to the graph of the differential equation's solution ( integral curve ) at each point ( x , y ) as a function of the point coordinates.

4. Folium of Descartes - Wikipedia

   en.wikipedia.org/wiki/Folium_of_Descartes

   The curve was first proposed and studied by René Descartes in 1638. [1] Its claim to fame lies in an incident in the development of calculus.Descartes challenged Pierre de Fermat to find the tangent line to the curve at an arbitrary point since Fermat had recently discovered a method for finding tangent lines.

5. Curve sketching - Wikipedia

   en.wikipedia.org/wiki/Curve_sketching

   If the curve passes through the origin then determine the tangent lines there. For algebraic curves, this can be done by removing all but the terms of lowest order from the equation and solving. Similarly, removing all but the terms of highest order from the equation and solving gives the points where the curve meets the line at infinity.

6. Envelope (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Envelope_(mathematics)

   Geometrically, the graph of v(x) is everywhere tangent to the graph of some member of the family u(x;a). Since the differential equation is first order, it only puts a condition on the tangent plane to the graph, so that any function everywhere tangent to a solution must also be a solution.

7. Graph of a function - Wikipedia

   en.wikipedia.org/wiki/Graph_of_a_function

   Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.