What is the extreme f(x)=x^2+x+y^2-4y ?

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

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extreme f(x)=x^2+x+y^2-4y

extreme points

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

Minimum (- \frac{1}{2}, 2)

Solution steps

Find the critical points:

(- \frac{1}{2}, 2)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(- \frac{1}{2}, 2) :

Minimum

Minimum (- \frac{1}{2}, 2)

G (x, y) = 40000 x + 30000 y - 8 x^{2} - 15 y^{2} - 10 x y

f (x, y) = x^{3} - 9 x y + y^{3}

y = f (x) = - x (x - 1)^{5}

f (x) = \frac{12}{x} + 3 π x^{2}

f (x) = x^{\frac{4}{7}} (\frac{11}{4} + x)

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