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

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

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

extreme points

f (x) = 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) = 4 - 2 (x - 1)^{\frac{2}{3}}

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

f (x) = 10 + x^{3} - \frac{9 x ^{2}}{2}

f (x) = 5 x + 10 sin (x)

f (x, y) = - 8 x^{3} y + 2 x y^{2} - 5 x^{2} y^{5} + 12 x

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