What is the extreme f(x,y)=5x^2+6y^2-10x-12y+14 ?

The extreme f(x,y)=5x^2+6y^2-10x-12y+14 is Minimum(1,1)

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extreme f(x,y)=5x^2+6y^2-10x-12y+14

extreme points

f (x, y) = 5 x^{2} + 6 y^{2} - 10 x - 12 y + 14

Minimum (1, 1)

Solution steps

Find the critical points:

(1, 1)

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

D (x, y) = 120

Check the sign of at each critical point

Check critical point

(1, 1) :

Minimum

Minimum (1, 1)

- 2 x^{2} y + 6 x^{2} + 4 y^{2} - 16 y + 16

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

f (x) = \frac{x ^{2} + 7 x + 3}{x + 2}

(5 + x)^{5}

f (x) = (x - 6) (x - 4)

What is the extreme f(x,y)=5x^2+6y^2-10x-12y+14 ?
The extreme f(x,y)=5x^2+6y^2-10x-12y+14 is Minimum(1,1)