extreme f(x,y)=sqrt(9-x^2-2y^2)

解答

极值点

f (x, y) = 9 - x^{2} - 2 y^{2}

极大值 (0, 0)

求解步骤

找到临界点:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{2 ( 9 - x ^{2} )}{( 9 - x ^{2} - 2 y ^{2} ) 9 - x ^{2} - 2 y ^{2}}

D (x, y) = \frac{18}{( - x ^{2} + 9 - 2 y ^{2} ) ^{2}}

检查在每个临界点处的符号

检查临界点

(0, 0) :

极大值

极大值 (0, 0)