匿名使用者
匿名使用者 發問時間: 科學數學 · 1 0 年前

兩題微積分

1.w^2+wsin(xyz)=0

發現W函數對X做偏微分

2.determine the relative extrema and saddle points of f(x,y)=x^3+y^3+3xy-2

求詳解 謝謝

1 個解答

評分
  • 1 0 年前
    最佳解答

    1. w^2 + wsin(xyz) = 0

    w = -sin(xyz)

    wx = -yzcos(xyz)

    2. f(x,y) = x^3 + y^3 + 3xy - 2

    fx = 3x^2 + 3y, fy = 3y^2 + 3x

    fxx = 6x, fyy = 6y, fxy = 3

    Put fx = fy = 0

    x^2 = -y or y^2 = -x

    We get y^2 = x^4

    So, x^4 + x = 0

    x(x^3 + 1) = 0

    x = 0 or -1

    For x = 0, y = 0. For x = -1, -1

    For (0,0), fxxfyy - (fxy)^2 = (0)(0) - (3)^2 = -9 < 0

    For (-1,-1), fxxfyy - (fxy)^2 = (-6)(-6) - (3)^2 = 27 > 0

    And fxx = -6 < 0

    So, (0,0) is a saddle point

    (-1,-1) is a maximum point.

    參考資料: Physics king
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