题目
题目
单项选择题

Question at position 2 The function f(x,y)=13x3+12y2+xy−6x+3f\left(x,y\right)=\frac{1}{3}x^3+\frac{1}{2}y^2+xy-6x+3 has a relative minimum at(-2, 2)(2, -2)(-3, 3)(2, 2)(3, -3)

选项
A.(-2, 2)
B.(2, -2)
C.(-3, 3)
D.(2, 2)
E.(3, -3)
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标准答案
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思路分析
Start by clearly identifying what the problem asks: locate relative minima of f(x,y) = (1/3)x^3 + (1/2)y^2 + xy − 6x + 3 and evaluate each given option as a potential critical point. Option 1: (-2, 2). Compute the partial derivatives: f_x = x^2 + y − 6 and f_y = y + x. At (-2, 2): f_x = (-2)^2 + 2 − 6 = 4 + 2 − 6 = 0, and f_y = 2 + (-2) = 0, so this is a critical point. Next, examine the Hessian: f_xx = 2x......Login to view full explanation

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Question at position 2 The function f(x,y)=13x3+12y2+xy−6x+3 has a relative minimum at(-2, 2)(-3, 3)(2, -2)(3, -3)(2, 2)

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