What is the extreme x^2+2y^2-2x-12y+19 ?

The extreme x^2+2y^2-2x-12y+19 is Minimum(1,3)

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extreme x^2+2y^2-2x-12y+19

extreme points

x^{2} + 2 y^{2} - 2 x - 12 y + 19

Minimum (1, 3)

Solution steps

Find the critical points:

(1, 3)

\frac{\partial ^{2} f}{\partial x ^{2}} = 4

D (x, y) = 8

Check the sign of at each critical point

Check critical point

(1, 3) :

Minimum

Minimum (1, 3)

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

f (x) = 2 x^{3} - 12 x^{2} + 18 x + 5

f (x) = 2 x \cdot ln (x)

f (x) = 5 x^{\frac{1}{3}} - x^{\frac{5}{3}}

6 x^{2} + 30 x - 84

What is the extreme x^2+2y^2-2x-12y+19 ?
The extreme x^2+2y^2-2x-12y+19 is Minimum(1,3)