What is the extreme f(x,y)=(x-y)(25-xy) ?

The extreme f(x,y)=(x-y)(25-xy) is Saddle(5,5),Saddle(-5,-5)

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extreme f(x,y)=(x-y)(25-xy)

extreme points

f (x, y) = (x - y) (25 - x y)

Saddle (5, 5), Saddle (- 5, - 5)

Solution steps

Find the critical points:

(5, 5), (- 5, - 5)

\frac{\partial ^{2} f}{\partial x ^{2}} = 2 x

D (x, y) = - 4 x^{2} + 4 x y - 4 y^{2}

Check the sign of at each critical point

Check critical point

(5, 5) :

Saddle

Check critical point

(- 5, - 5) :

Saddle

Saddle (5, 5), Saddle (- 5, - 5)

f (x) = x^{3} - y^{3} - 2 x y + 6

f (x) = x y + \frac{3}{x} + \frac{9}{y}

f (x) = - 8 x^{2} + 8 x

\frac{e ^{- x}}{( 1 + e ^{- x} ) ^{2}}

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

What is the extreme f(x,y)=(x-y)(25-xy) ?
The extreme f(x,y)=(x-y)(25-xy) is Saddle(5,5),Saddle(-5,-5)