What is the extreme f(x)=3x^2+5y^2-10xy-6y+1 ?

The extreme f(x)=3x^2+5y^2-10xy-6y+1 is Saddle(-3/2 ,-9/10)

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extreme f(x)=3x^2+5y^2-10xy-6y+1

extreme points

f (x) = 3 x^{2} + 5 y^{2} - 10 x y - 6 y + 1

Saddle (- \frac{3}{2}, - \frac{9}{10})

Solution steps

Find the critical points:

(- \frac{3}{2}, - \frac{9}{10})

\frac{\partial ^{2} f}{\partial x ^{2}} = 10

D (x, y) = - 40

Check the sign of at each critical point

Check critical point

(- \frac{3}{2}, - \frac{9}{10}) :

Saddle

Saddle (- \frac{3}{2}, - \frac{9}{10})

9600 + 280 x - 10 x^{2}

4 x^{3} + 9 x^{2} - 54 x + 6

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

f (x) = x^{5} - 10 x^{4} - 1 = x^{4} (x - 10) - 1

What is the extreme f(x)=3x^2+5y^2-10xy-6y+1 ?
The extreme f(x)=3x^2+5y^2-10xy-6y+1 is Saddle(-3/2 ,-9/10)