What is the extreme 2y^2+2xy+x^2-16x-20y ?

The extreme 2y^2+2xy+x^2-16x-20y is Minimum(2,6)

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extreme 2y^2+2xy+x^2-16x-20y

extreme points

2 y^{2} + 2 x y + x^{2} - 16 x - 20 y

Minimum (2, 6)

Solution steps

Find the critical points:

(2, 6)

\frac{\partial ^{2} f}{\partial y ^{2}} = 2

D (y, x) = 4

Check the sign of at each critical point

Check critical point

(2, 6) :

Minimum

Minimum (2, 6)

f (x) = - 2 x^{2} + 200 x

y = x^{2} - 5 x - 14

x \cdot 7 - x

f (x) = - 5 x^{2} - 8 y^{2} - 2 x y + 102 y

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

What is the extreme 2y^2+2xy+x^2-16x-20y ?
The extreme 2y^2+2xy+x^2-16x-20y is Minimum(2,6)