题目

f(x,y)=x^2-2xy^2+2y^4-2y^2是否有极值,如果有,极值为?

提问时间：2021-04-29

答案

f(x,y)=x^2-2xy^2+2y^4-2y^2求一阶偏导：∂f/∂x=2x-2y^2=0∂f/∂y=-4xy+8y^3-4y=0得：x-y^2=0xy-2y^3+y=0再化简：xy-y^3-y^3+y=0y(x-y^2)-y^3+y=00+y(y^2-1)=0y*(y-1)*(y+1)=0解得：y=±1,0x= ...