What is the extreme x^2+xy+y^2-25y+208 ?

The extreme x^2+xy+y^2-25y+208 is Minimum(-25/3 , 50/3)

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extreme x^2+xy+y^2-25y+208

extreme points

x^{2} + x y + y^{2} - 25 y + 208

Minimum (- \frac{25}{3}, \frac{50}{3})

Solution steps

Find the critical points:

(- \frac{25}{3}, \frac{50}{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{25}{3}, \frac{50}{3}) :

Minimum

Minimum (- \frac{25}{3}, \frac{50}{3})

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 11

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

f (x) = - (x^{2} + x)^{\frac{2}{3}}, - 2 \leq x \leq 3

52900 + 400 x + x^{2}

f (x) = - x - 4, - 4 \leq x \leq 1

What is the extreme x^2+xy+y^2-25y+208 ?
The extreme x^2+xy+y^2-25y+208 is Minimum(-25/3 , 50/3)