What is the extreme f(x,y,λ)=9-x^2-y^2+λ(4-x-y) ?

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

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extreme f(x,y,λ)=9-x^2-y^2+λ(4-x-y)

extreme points

f (x, y, λ) = 9 - x^{2} - y^{2} + λ (4 - x - y)

Maximum (- \frac{λ}{2}, - \frac{λ}{2})

Solution steps

Find the critical points:

(- \frac{λ}{2}, - \frac{λ}{2})

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(- \frac{λ}{2}, - \frac{λ}{2}) :

Maximum

Maximum (- \frac{λ}{2}, - \frac{λ}{2})

\frac{1 - x}{x ^{2} + 3}

g (t) = u^{1} (t) + 2 u^{3} (t) - 6 u^{4} (t)

f (x) = ∣ x ∣ + x^{2} - 5 x + 6, (- 1, 4)

f (x, y) = 7 x^{2} + 6 x y + 5 y^{2} + 4 x y^{2} + 7 x^{2} y

x^{2} + x y + y^{2} + 8 y

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