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Implicit Relations

Exploring the behaviors of implicit relations.

Mapped to AP College Board # FUN-4, FUN-4.D, FUN-4.D.1, FUN-4.E, FUN-4.E.1, FUN-4.E.2

A function’s derivative can be used to understand some behaviors of the function. Determine critical points of implicit relations. A point on an implicit relation where the first derivative equals zero or does not exist is a critical point of the function. Justify conclusions about the behavior of an implicitly defined function based on evidence from its derivatives. Applications of derivatives can be extended to implicitly defined functions. Second derivatives involving implicit differentiation may be relations of x, y, and dy/dx.