What is the extreme f(x)=x^2+xy+1/2 y^2-3x+y ?

The extreme f(x)=x^2+xy+1/2 y^2-3x+y is Minimum(4,-5)

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extreme f(x)=x^2+xy+1/2 y^2-3x+y

extreme points

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

Minimum (4, - 5)

Solution steps

Find the critical points:

(4, - 5)

\frac{\partial ^{2} f}{\partial x ^{2}} = 1

D (x, y) = 1

Check the sign of at each critical point

Check critical point

(4, - 5) :

Minimum

Minimum (4, - 5)

x^{2} + \frac{400}{x}

0.05 x + 20 + \frac{125}{x}

f (x) = \frac{9 ( t - 2 ) ^{2}}{t ^{2}}

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

e^{2 x}

What is the extreme f(x)=x^2+xy+1/2 y^2-3x+y ?
The extreme f(x)=x^2+xy+1/2 y^2-3x+y is Minimum(4,-5)