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Critical Point

A Function $y = f(x)$ has critical points at all points $x_0$ where $f'(x_0) = 0$ or $f(x)$ is not Differentiable. A Function $z = f(x,y)$ has critical points where the Gradient $\nabla f = {\bf0}$ or ${\partial f/\partial x}$ or the Partial Derivative ${\partial f/\partial y}$ is not defined.

See also Fixed Point, Inflection Point, Only Critical Point in Town Test, Stationary Point

© 1996-9 Eric W. Weisstein