What is the extreme 3x^2-xy+5y^2 ?

The extreme 3x^2-xy+5y^2 is Minimum(0,0)

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extreme 3x^2-xy+5y^2

extreme points

3 x^{2} - x y + 5 y^{2}

Minimum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 10

D (x, y) = 59

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Minimum (0, 0)

f (x) = - x^{3} - 9 x^{2} + 4

x^{2} + 1 + e^{x y}

f (x, y) = y + 81 - x^{2} - y^{2}

f (x) = \frac{2 x ^{3}}{3} + \frac{7 x ^{2}}{2} - 4 x

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