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

The extreme f(x,y)=5-(x-6)^2-(y+2)^2 is Maximum(6,-2)

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

extreme points

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

Maximum (6, - 2)

Solution steps

Find the critical points:

(6, - 2)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(6, - 2) :

Maximum

Maximum (6, - 2)

2 (x + 5)

r (x)

f (x) = \frac{2 x ( x ^{2} - 6 x )}{( x - 2 ) ^{2}}

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

f (x) = \frac{( x ^{2} )}{x ^{2} - 1}

What is the extreme f(x,y)=5-(x-6)^2-(y+2)^2 ?
The extreme f(x,y)=5-(x-6)^2-(y+2)^2 is Maximum(6,-2)