What is the extreme f(x,y)=7xy+14x-x^2+2y^2 ?

The extreme f(x,y)=7xy+14x-x^2+2y^2 is Saddle(56/57 ,-98/57)

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extreme f(x,y)=7xy+14x-x^2+2y^2

extreme points

f (x, y) = 7 x y + 14 x - x^{2} + 2 y^{2}

Saddle (\frac{56}{57}, - \frac{98}{57})

Solution steps

Find the critical points:

(\frac{56}{57}, - \frac{98}{57})

\frac{\partial ^{2} f}{\partial x ^{2}} = 4

D (x, y) = - 57

Check the sign of at each critical point

Check critical point

(\frac{56}{57}, - \frac{98}{57}) :

Saddle

Saddle (\frac{56}{57}, - \frac{98}{57})

4 x^{2} - 8 x^{4}

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

f (x) = 9 x^{3} + 21 x^{2} + 8 x - 3

f (x) = x^{2} - 2 x + 5 [- 1.4]

2 x^{4} - 196 x^{2} - 3

What is the extreme f(x,y)=7xy+14x-x^2+2y^2 ?
The extreme f(x,y)=7xy+14x-x^2+2y^2 is Saddle(56/57 ,-98/57)