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  2. Derivative test - Wikipedia

    en.wikipedia.org/wiki/Derivative_test

    After establishing the critical points of a function, the second-derivative test uses the value of the second derivative at those points to determine whether such points are a local maximum or a local minimum. [1] If the function f is twice-differentiable at a critical point x (i.e. a point where f ′ (x) = 0), then:

  3. Critical point (mathematics) - Wikipedia

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

    A critical point of a function of a single real variable, f (x), is a value x 0 in the domain of f where f is not differentiable or its derivative is 0 (i.e. ′ =). [2] A critical value is the image under f of a critical point.

  4. Fermat's theorem (stationary points) - Wikipedia

    en.wikipedia.org/wiki/Fermat's_theorem...

    Fermat's theorem is central to the calculus method of determining maxima and minima: in one dimension, one can find extrema by simply computing the stationary points (by computing the zeros of the derivative), the non-differentiable points, and the boundary points, and then investigating this set to determine the extrema.

  5. Saddle point - Wikipedia

    en.wikipedia.org/wiki/Saddle_point

    A saddle point (in red) on the graph of z = x 2 − y 2 (hyperbolic paraboloid). In mathematics, a saddle point or minimax point [1] is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function. [2]

  6. Second partial derivative test - Wikipedia

    en.wikipedia.org/wiki/Second_partial_derivative_test

    At the remaining critical point (0, 0) the second derivative test is insufficient, and one must use higher order tests or other tools to determine the behavior of the function at this point. (In fact, one can show that f takes both positive and negative values in small neighborhoods around (0, 0) and so this point is a saddle point of f.)

  7. Critical exponent - Wikipedia

    en.wikipedia.org/wiki/Critical_exponent

    Close enough to the critical point, everything can be reexpressed in terms of certain ratios of the powers of the reduced quantities. These are the scaling functions. The origin of scaling functions can be seen from the renormalization group. The critical point is an infrared fixed point. In a sufficiently small neighborhood of the critical ...

  8. Critical point (set theory) - Wikipedia

    en.wikipedia.org/wiki/Critical_point_(set_theory)

    If () = for all < and () >, then is said to be the critical point of . If N {\displaystyle N} is V , then κ {\displaystyle \kappa } (the critical point of j {\displaystyle j} ) is always a measurable cardinal , i.e. an uncountable cardinal number κ such that there exists a κ {\displaystyle \kappa } -complete, non-principal ultrafilter over ...

  9. Critical point - Wikipedia

    en.wikipedia.org/wiki/Critical_point

    Critical point may refer to: Critical phenomena in physics; Critical point (mathematics), in calculus, a point where a function's derivative is either zero or nonexistent; Critical point (set theory), an elementary embedding of a transitive class into another transitive class which is the smallest ordinal which is not mapped to itself