What is the extreme f(x,y)=2-5x^2-2y^2 ?

The extreme f(x,y)=2-5x^2-2y^2 is Maximum(0,0)

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extreme f(x,y)=2-5x^2-2y^2

extreme points

f (x, y) = 2 - 5 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) = 40

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

f (x, y) = ln (9 - x^{2} - y^{2})

y = 4 - x^{2}

2 cos (x) + sin (2 x)

f (x) = x^{3} - 18 x^{2} + 81 x + 45

2 x^{3} - 6 x^{2} - 18 x

What is the extreme f(x,y)=2-5x^2-2y^2 ?
The extreme f(x,y)=2-5x^2-2y^2 is Maximum(0,0)