求函数f(x,y)=e的x-y次方乘以(x的平方-2y的平方)的极值

题目

求函数f(x,y)=e的x-y次方乘以(x的平方-2y的平方)的极值

答案

f(x,y)=e^(x-y)(x²-2y²)f`x=e^(x-y)(x²-2y²)+2xe^(x-y) =e^(x-y)(x²-2y²+2x)=0x²-2y²+2x=0f`y=e^(x-y)(-1)(x²-2y²)-4ye^(x-y) =e^(x-y)(-x²+2y²-4...