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

The extreme f(x,y)=3xy^2-2y+5x^2y^2 is Saddle(-3/10 ,-20/9)

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

extreme points

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

Saddle (- \frac{3}{10}, - \frac{20}{9})

Solution steps

Find the critical points:

(- \frac{3}{10}, - \frac{20}{9})

\frac{\partial ^{2} f}{\partial x ^{2}} = 10 x^{2} + 6 x

D (x, y) = - 300 x^{2} y^{2} - 180 x y^{2} - 36 y^{2}

Check the sign of at each critical point

Check critical point

(- \frac{3}{10}, - \frac{20}{9}) :

Saddle

Saddle (- \frac{3}{10}, - \frac{20}{9})

What is the extreme f(x,y)=3xy^2-2y+5x^2y^2 ?
The extreme f(x,y)=3xy^2-2y+5x^2y^2 is Saddle(-3/10 ,-20/9)