What is the extreme f(x,y)=3+sqrt(1-((x-2)^2)/4-((y-3)^2)/9) ?

The extreme f(x,y)=3+sqrt(1-((x-2)^2)/4-((y-3)^2)/9) is Maximum(2,3)

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extreme f(x,y)=3+sqrt(1-((x-2)^2)/4-((y-3)^2)/9)

extreme points

f (x, y) = 3 + 1 - \frac{( x - 2 ) ^{2}}{4} - \frac{( y - 3 ) ^{2}}{9}

Maximum (2, 3)

Solution steps

Find the critical points:

(2, 3)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{6 x ( x - 4 )}{( - 9 x ^{2} + 36 x + 24 y - 4 y ^{2} - 36 ) - 9 x ^{2} + 36 x + 24 y - 4 y ^{2} - 36}

D (x, y) = \frac{36}{( - 36 - 9 x ^{2} - 4 y ^{2} + 24 y + 36 x ) ^{2}}

Check the sign of at each critical point

Check critical point

(2, 3) :

Maximum

Maximum (2, 3)

f (x) = \frac{x ^{2}}{2} + \frac{1}{3} x

y = x^{4} - 4 x^{3}

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

x^{3} - 3 x^{2}

f (x, y) = ∣ x y ∣

What is the extreme f(x,y)=3+sqrt(1-((x-2)^2)/4-((y-3)^2)/9) ?
The extreme f(x,y)=3+sqrt(1-((x-2)^2)/4-((y-3)^2)/9) is Maximum(2,3)