What is the extreme 3x^2+y^2-xy-11x ?

The extreme 3x^2+y^2-xy-11x is Minimum(2,1)

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extreme 3x^2+y^2-xy-11x

extreme points

3 x^{2} + y^{2} - x y - 11 x

Minimum (2, 1)

Solution steps

Find the critical points:

(2, 1)

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

D (x, y) = 11

Check the sign of at each critical point

Check critical point

(2, 1) :

Minimum

Minimum (2, 1)

x^{2} - 8 x

f (x) = - x^{3} - 6 x^{2} - 9 x + 3

f (x) = x^{3} - 6 x^{2} + 3

f (x) = x^{2} + 9

\frac{4}{x + 6}

What is the extreme 3x^2+y^2-xy-11x ?
The extreme 3x^2+y^2-xy-11x is Minimum(2,1)