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

The extreme f(x,y)=9y^2-3x^2-10y+5xy is Saddle(50/133 , 60/133)

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extreme f(x,y)=9y^2-3x^2-10y+5xy

extreme points

f (x, y) = 9 y^{2} - 3 x^{2} - 10 y + 5 x y

Saddle (\frac{50}{133}, \frac{60}{133})

Solution steps

Find the critical points:

(\frac{50}{133}, \frac{60}{133})

\frac{\partial ^{2} f}{\partial x ^{2}} = 18

D (x, y) = - 133

Check the sign of at each critical point

Check critical point

(\frac{50}{133}, \frac{60}{133}) :

Saddle

Saddle (\frac{50}{133}, \frac{60}{133})

f (x) = x^{3} - 5 x^{2} + 3 x + 12, (- 2, 4)

f (x) = - 4 x^{2} + 16 x - 3, - 4 \leq x \leq 4

f (x, y) = - 294 \cdot x + 2 \cdot x^{3} + 6 \cdot x \cdot y^{2} - 3 \cdot y^{3}

f (x) = ln (x y - 6)

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

What is the extreme f(x,y)=9y^2-3x^2-10y+5xy ?
The extreme f(x,y)=9y^2-3x^2-10y+5xy is Saddle(50/133 , 60/133)