设y=f(x)由方程2y^3-2y^2+2xy-x^2=1所确定,试求y=f(x)的极值.
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![设y=f(x)由方程2y^3-2y^2+2xy-x^2=1所确定,试求y=f(x)的极值.](/uploads/image/z/290431-55-1.jpg?t=%E8%AE%BEy%3Df%28x%29%E7%94%B1%E6%96%B9%E7%A8%8B2y%5E3-2y%5E2%2B2xy-x%5E2%3D1%E6%89%80%E7%A1%AE%E5%AE%9A%2C%E8%AF%95%E6%B1%82y%3Df%28x%29%E7%9A%84%E6%9E%81%E5%80%BC.)
设y=f(x)由方程2y^3-2y^2+2xy-x^2=1所确定,试求y=f(x)的极值.
设y=f(x)由方程2y^3-2y^2+2xy-x^2=1所确定,试求y=f(x)的极值.
设y=f(x)由方程2y^3-2y^2+2xy-x^2=1所确定,试求y=f(x)的极值.
求导得:6y²y'-4yy'+2y+2xy'-2x=0
3y²y'-2yy'+y+xy'-x=0
y‘(3y²-2y+x)=x-y
y'=(x-y)/(3y²-2y+x)
极值,则:y'=0,得:x=y
把y=x代入方程:2y³-2y²+2xy-x²=1得:2x³-2x²+2x²-x²=1
2x³-x²=1
x³-x²+x³-1=0
x²(x-1)+(x-1)(x²+x+1)=0
(x-1)(2x²+x+1)=0
得:x=1
则:y=1
所以,极值为1