What is the extreme f(x,y)=xy-7xy+200x ?

The extreme f(x,y)=xy-7xy+200x is Saddle(0, 100/3)

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extreme f(x,y)=xy-7xy+200x

extreme points

f (x, y) = x y - 7 x y + 200 x

Saddle (0, \frac{100}{3})

Solution steps

Find the critical points:

(0, \frac{100}{3})

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 36

Check the sign of at each critical point

Check critical point

(0, \frac{100}{3}) :

Saddle

Saddle (0, \frac{100}{3})

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

f (x) = \frac{x - 1}{x ^{2}}

f (x, y) = - 5 x^{2} + 4 x y - y^{2} + 16 x + 10

f (x, y) = \frac{y}{x}

f (x, y) = \frac{x ^{2} - 5 y ^{2}}{x + 4}

What is the extreme f(x,y)=xy-7xy+200x ?
The extreme f(x,y)=xy-7xy+200x is Saddle(0, 100/3)