What is the extreme f(x,y)=x^2+xy+y^2-34y+385 ?

The extreme f(x,y)=x^2+xy+y^2-34y+385 is Minimum(-34/3 , 68/3)

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extreme f(x,y)=x^2+xy+y^2-34y+385

extreme points

f (x, y) = x^{2} + x y + y^{2} - 34 y + 385

Minimum (- \frac{34}{3}, \frac{68}{3})

Solution steps

Find the critical points:

(- \frac{34}{3}, \frac{68}{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{34}{3}, \frac{68}{3}) :

Minimum

Minimum (- \frac{34}{3}, \frac{68}{3})

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

f (x) = x - 2 x

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

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

4 x^{3} - 3 x^{2} - 6 x + 3

What is the extreme f(x,y)=x^2+xy+y^2-34y+385 ?
The extreme f(x,y)=x^2+xy+y^2-34y+385 is Minimum(-34/3 , 68/3)