What is the extreme f(x,y)=3x^2+8xy-7y^2-3x+6y ?

The extreme f(x,y)=3x^2+8xy-7y^2-3x+6y is Saddle(-3/74 , 15/37)

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extreme f(x,y)=3x^2+8xy-7y^2-3x+6y

extreme points

f (x, y) = 3 x^{2} + 8 x y - 7 y^{2} - 3 x + 6 y

Saddle (- \frac{3}{74}, \frac{15}{37})

Solution steps

Find the critical points:

(- \frac{3}{74}, \frac{15}{37})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 14

D (x, y) = - 148

Check the sign of at each critical point

Check critical point

(- \frac{3}{74}, \frac{15}{37}) :

Saddle

Saddle (- \frac{3}{74}, \frac{15}{37})

f (x, y) = x^{2} - 4 x - y^{2} - 6 y + 7

f (x) = x^{5} - 5 x^{4} + 5 = x^{4} (x - 5) + 5

f (x) = - x^{2} + 12 x + 80

f (x) = x \cdot (4 - 2 x) \cdot (11 - 2 x)

x^{3} + y^{3} - 3 x^{2} - 9 y^{2} - 9 x

What is the extreme f(x,y)=3x^2+8xy-7y^2-3x+6y ?
The extreme f(x,y)=3x^2+8xy-7y^2-3x+6y is Saddle(-3/74 , 15/37)