What is the extreme f(x,y)=-6x^2+4y^2+2x+4y+8 ?

The extreme f(x,y)=-6x^2+4y^2+2x+4y+8 is Saddle(1/6 ,-1/2)

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extreme f(x,y)=-6x^2+4y^2+2x+4y+8

extreme points

f (x, y) = - 6 x^{2} + 4 y^{2} + 2 x + 4 y + 8

Saddle (\frac{1}{6}, - \frac{1}{2})

Solution steps

Find the critical points:

(\frac{1}{6}, - \frac{1}{2})

\frac{\partial ^{2} f}{\partial x ^{2}} = 8

D (x, y) = - 96

Check the sign of at each critical point

Check critical point

(\frac{1}{6}, - \frac{1}{2}) :

Saddle

Saddle (\frac{1}{6}, - \frac{1}{2})

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

f (x, y) = 2 x^{2} + 4 x y + y^{2} + 5

P (x, y) = 6 x^{2} + 19 x y + 15 y^{2} - 17 y - 11 x + 4

5 sin^{2} (x), 0 \leq x \leq π

f (x) = - x^{3} + 3 x - 11

What is the extreme f(x,y)=-6x^2+4y^2+2x+4y+8 ?
The extreme f(x,y)=-6x^2+4y^2+2x+4y+8 is Saddle(1/6 ,-1/2)