What is the extreme f(x,y)=x^2+xy+y^2-37y+456 ?

The extreme f(x,y)=x^2+xy+y^2-37y+456 is Minimum(-37/3 , 74/3)

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extreme f(x,y)=x^2+xy+y^2-37y+456

extreme points

f (x, y) = x^{2} + x y + y^{2} - 37 y + 456

Minimum (- \frac{37}{3}, \frac{74}{3})

Solution steps

Find the critical points:

(- \frac{37}{3}, \frac{74}{3})

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(- \frac{37}{3}, \frac{74}{3}) :

Minimum

Minimum (- \frac{37}{3}, \frac{74}{3})

f (x) = x^{3} + 3 x^{2} + 3 x - 4

y = x 25 - x^{2}

f (x) = x^{6} + \frac{6}{x}

f (x) = 8 x y - x^{3} - 4 y^{2}

f (θ) = - 5 cos (\frac{3}{4} θ - 6) - 2

What is the extreme f(x,y)=x^2+xy+y^2-37y+456 ?
The extreme f(x,y)=x^2+xy+y^2-37y+456 is Minimum(-37/3 , 74/3)