| DescriptionImplicit Function Theorem.svg |
Demonstration of the Implicit Function Theorem. The curves are the implicitly defined as  with various values of the constant  . The background slope field shows that if one is given a point on the curve then one can, in principle, generate a local piece of the curve defined as an explicit function of x, or at least approximate it by tracing from slope field (e.g. approximation by Euler's method which can be made as accurate as desired by choosing small step size; as step size approaches zero the result matches the actual local piece of curve more accurately). |
