extreme f(x,y)=sqrt(49-(x-9)^2-y^2)

解答

极值点

f (x, y) = 49 - (x - 9)^{2} - y^{2}

极大值 (9, 0)

求解步骤

找到临界点:

(9, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{- x ^{2} + 18 x - 32}{( - x ^{2} + 18 x - y ^{2} - 32 ) - x ^{2} + 18 x - y ^{2} - 32}

D (x, y) = \frac{49}{( x ^{2} - 18 x + y ^{2} + 32 ) ^{2}}

检查在每个临界点处的符号

检查临界点

(9, 0) :

极大值

极大值 (9, 0)

e x t re m e f (x) = 4 x^{2} - 5 x - 2

e x t re m e f (x, y) = x y - 2 x - 4 y

e x t re m e f (x) = x^{3} - 4 x^{2} - 3 x + 8

e x t re m e 2 x^{3} - 6 x^{2} + 6 x + 1

e x t re m e f (x) = 9 + 4 x^{2} - x^{4}