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, y) = 3 x^{2} - y^{2}

3 x^{5} - 5 x^{3} + 1

f (x) = 2 sin (x) - cos (2 x), 0 \leq x \leq 2 π

f (x) = 2 x^{2} + 3 x y + 4 y^{2} - 2 x + 10 y

f (x) = x^{4} - 8 x^{3} - 6

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)