loveyoudx 發問於 科學及數學數學 · 1 十年前

about Partial Differentiation

what's difference betwen saddle point, critical point and local examum?

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  • 1 十年前
    最愛解答

    A critical point is a point on the domain of a function where the derivative is equal to zero or does not exist. It is also called a stationary point. Critical points include saddle points and local extremums.

    In one or several variables, the local extremum (maximum or minimum) of a function (if they exist) can occur either at its critical points or at points on its boundary, or points where the function is not differentiable. They are points in the domain of a function at which the function takes a largest value (maximum) or smallest value (minimum), either within a given neighbourhood (local extremum) or on the function domain in its entirety (global extremum).

    圖片參考:http://upload.wikimedia.org/wikipedia/en/thumb/4/4...

    A critical point is sometimes not a local maximum or minimum. In that case it is called a saddle point.

    A saddle point is a point such that the curve/surface/etc. in the neighborhood of this point lies on different sides of the tangent at this point.

    A saddle point is a point of a function (of one or more variables) which is both a stationary point and a point of inflection. Since it is a point of inflection, it is not a local extremum.

    The red point in the following figure is the saddle point.

    圖片參考:http://upload.wikimedia.org/wikipedia/commons/thum...

    資料來源: wiki
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