题目
题目
单项选择题

Question at position 1 The number of critical points of f(x,y)=x2+x2y+y2−2y+2f\left(x,y\right)=x^2+x^2y+y^2-2y+2 is42301

选项
A.4
B.2
C.3
D.0
E.1
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标准答案
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思路分析
We start by examining the function: f(x,y) = x^2 + x^2 y + y^2 - 2y + 2. To find critical points, we compute the partial derivatives: - f_x = ∂f/∂x = 2x + 2xy = 2x(1 + y). - f_y = ∂f/∂y = x^2 + 2y - 2. Critical points satisfy f_x = 0 and f_y = 0. From f_x = 0, we have two cases: either x = 0 or y = -1. Case A: x = 0.......Login to view full explanation

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