What is the extreme x^2+xy+y^2-28y+261 ?

The extreme x^2+xy+y^2-28y+261 is Minimum(-28/3 , 56/3)

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extreme x^2+xy+y^2-28y+261

extreme points

x^{2} + x y + y^{2} - 28 y + 261

Minimum (- \frac{28}{3}, \frac{56}{3})

Solution steps

Find the critical points:

(- \frac{28}{3}, \frac{56}{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{28}{3}, \frac{56}{3}) :

Minimum

Minimum (- \frac{28}{3}, \frac{56}{3})

f (x) = 2 x - 13 ln (4 x)

f (x) = \frac{x ^{\frac{5}{3}}}{2 + x}, - 1 \leq x \leq 8

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

1. 3^{x}

f (x) = x^{3} - 2 x^{2} - 15 x + 5, - 2 \leq x \leq 0

What is the extreme x^2+xy+y^2-28y+261 ?
The extreme x^2+xy+y^2-28y+261 is Minimum(-28/3 , 56/3)