What is the extreme f(x,y)=(9x^2+7x+10)(9y^2+4y+9) ?

The extreme f(x,y)=(9x^2+7x+10)(9y^2+4y+9) is Minimum(-7/18 ,-2/9)

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extreme f(x,y)=(9x^2+7x+10)(9y^2+4y+9)

extreme points

f (x, y) = (9 x^{2} + 7 x + 10) (9 y^{2} + 4 y + 9)

Minimum (- \frac{7}{18}, - \frac{2}{9})

Solution steps

Find the critical points:

(- \frac{7}{18}, - \frac{2}{9})

\frac{\partial ^{2} f}{\partial x ^{2}} = 18 (9 x^{2} + 7 x + 10)

D (x, y) = 21060 x^{2} - 78732 x^{2} y^{2} - 34992 x^{2} y + 16380 x - 61236 x y^{2} - 27216 x y + 13284 y^{2} + 5904 y + 28376

Check the sign of at each critical point

Check critical point

(- \frac{7}{18}, - \frac{2}{9}) :

Minimum

Minimum (- \frac{7}{18}, - \frac{2}{9})

f (x) = 4 x^{2} - 2 x + 1

a + (ln (x))^{2}

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

f (x, y) = x^{3} - 4 x^{2} - 4 y^{2} + 8 x y - 3 x

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

What is the extreme f(x,y)=(9x^2+7x+10)(9y^2+4y+9) ?
The extreme f(x,y)=(9x^2+7x+10)(9y^2+4y+9) is Minimum(-7/18 ,-2/9)