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

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

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

extreme points

f (x) = (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, y) = x^{2} y - 3 x y + 5 y

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

f (x) = x^{4} - 4 x + 7

f (x) = 400 - \frac{3600}{x + 8} - x

f (x) = 3 x^{2} - 2 x^{2} - 5 x + 6

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