What is the extreme T(x,y)=50-6x^2-2y^2 ?

The extreme T(x,y)=50-6x^2-2y^2 is Maximum(0,0)

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extreme T(x,y)=50-6x^2-2y^2

extreme points

T (x, y) = 50 - 6 x^{2} - 2 y^{2}

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = 48

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

f (x, y) = x^{2} y + 2 x y^{2} - 12 x y + 2

f (x, y) = 2 x^{3}

25 x^{2} - 260 x + 1700

x + \frac{31}{x}

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

What is the extreme T(x,y)=50-6x^2-2y^2 ?
The extreme T(x,y)=50-6x^2-2y^2 is Maximum(0,0)