What is the extreme f(x)=x^2+xy+y^2-16y+85 ?

The extreme f(x)=x^2+xy+y^2-16y+85 is Minimum(-16/3 , 32/3)

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extreme f(x)=x^2+xy+y^2-16y+85

extreme points

f (x) = x^{2} + x y + y^{2} - 16 y + 85

Minimum (- \frac{16}{3}, \frac{32}{3})

Solution steps

Find the critical points:

(- \frac{16}{3}, \frac{32}{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{16}{3}, \frac{32}{3}) :

Minimum

Minimum (- \frac{16}{3}, \frac{32}{3})

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

x + 1

f (x, y) = x^{2} + y^{2} - 8 y + 16

\frac{3 x - 6}{x + 2}

f (x, y) = \frac{1}{2} (x^{2} - y^{2})

What is the extreme f(x)=x^2+xy+y^2-16y+85 ?
The extreme f(x)=x^2+xy+y^2-16y+85 is Minimum(-16/3 , 32/3)