enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Maximum and minimum - Wikipedia

    en.wikipedia.org/wiki/Maximum_and_minimum

    Unique global maximum over the positive real numbers at x = 1/e. x 3 /3 − x: First derivative x 2 − 1 and second derivative 2x. Setting the first derivative to 0 and solving for x gives stationary points at −1 and +1. From the sign of the second derivative, we can see that −1 is a local maximum and +1 is a local minimum.

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

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

    Fermat's theorem gives only a necessary condition for extreme function values, as some stationary points are inflection points (not a maximum or minimum). The function's second derivative, if it exists, can sometimes be used to determine whether a stationary point is a maximum or minimum.

  4. Maximum modulus principle - Wikipedia

    en.wikipedia.org/wiki/Maximum_modulus_principle

    2.3 Using Cauchy's Integral Formula [1] 3 Physical interpretation. 4 Applications. 5 ... is a local maximum for this function also, it follows from the maximum ...

  5. Second partial derivative test - Wikipedia

    en.wikipedia.org/wiki/Second_partial_derivative_test

    Thus, the second partial derivative test indicates that f(x, y) has saddle points at (0, −1) and (1, −1) and has a local maximum at (,) since = <. 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.

  6. Local property - Wikipedia

    en.wikipedia.org/wiki/Local_property

    Perhaps the best-known example of the idea of locality lies in the concept of local minimum (or local maximum), which is a point in a function whose functional value is the smallest (resp., largest) within an immediate neighborhood of points. [1]

  7. Lagrange multiplier - Wikipedia

    en.wikipedia.org/wiki/Lagrange_multiplier

    The Lagrange multiplier theorem states that at any local maximum (or minimum) of the function evaluated under the equality constraints, if constraint qualification applies (explained below), then the gradient of the function (at that point) can be expressed as a linear combination of the gradients of the constraints (at that point), with the ...

  8. Critical point (mathematics) - Wikipedia

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

    A critical point (where the function is differentiable) may be either a local maximum, a local minimum or a saddle point. If the function is at least twice continuously differentiable the different cases may be distinguished by considering the eigenvalues of the Hessian matrix of second derivatives.

  9. Calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Calculus_of_Variations

    [e] The extremum [] is called a local maximum if everywhere in an arbitrarily small neighborhood of , and a local minimum if there. For a function space of continuous functions, extrema of corresponding functionals are called strong extrema or weak extrema , depending on whether the first derivatives of the continuous functions are respectively ...