What is the extreme f(x,y)=60x+6y+12xy-3x^2-6y^2+100 ?

The extreme f(x,y)=60x+6y+12xy-3x^2-6y^2+100 is Saddle(-11,-21/2)

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extreme f(x,y)=60x+6y+12xy-3x^2-6y^2+100

extreme points

f (x, y) = 60 x + 6 y + 12 x y - 3 x^{2} - 6 y^{2} + 100

Saddle (- 11, - \frac{21}{2})

Solution steps

Find the critical points:

(- 11, - \frac{21}{2})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 12

D (x, y) = - 72

Check the sign of at each critical point

Check critical point

(- 11, - \frac{21}{2}) :

Saddle

Saddle (- 11, - \frac{21}{2})

f (x) = x^{2} + 6 x + 11

f (x) = x^{2} + 6 x + 17

f (x) = x^{2} + 6 x + 16

f (x) = 4 x^{3} + 6 x^{2}

g (x) = 8 - 5 sin (x), 0 \leq x \leq π

What is the extreme f(x,y)=60x+6y+12xy-3x^2-6y^2+100 ?
The extreme f(x,y)=60x+6y+12xy-3x^2-6y^2+100 is Saddle(-11,-21/2)