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+2 is31240

选项
A.3
B.1
C.2
D.4
E.0
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标准答案
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思路分析
We start by interpreting the problem: find the number of critical points of the function f(x,y) = x^2 + x^2 y + y^2 - 2y + 2. First, compute the partial derivatives to locate critical points where the gradient is zero. - f_x = ∂f/∂x = 2x + ∂(x^2 y)/∂x = 2x + 2xy = 2x(1 + y). - f_y = ∂f/∂y = ∂(x^2 y)/∂y + ∂(y^2)/∂y + ∂(-2y)/∂y = x^2 + 2y - 2. ......Login to view full explanation

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