What is the extreme f(x,y)=x^2+y^2-4x+17x-10y+2021 ?

The extreme f(x,y)=x^2+y^2-4x+17x-10y+2021 is Minimum(-13/2 ,5)

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extreme f(x,y)=x^2+y^2-4x+17x-10y+2021

extreme points

f (x, y) = x^{2} + y^{2} - 4 x + 17 x - 10 y + 2021

Minimum (- \frac{13}{2}, 5)

Solution steps

Find the critical points:

(- \frac{13}{2}, 5)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(- \frac{13}{2}, 5) :

Minimum

Minimum (- \frac{13}{2}, 5)

f (x) = 18 x^{2} - 32 y^{2} - 36 x - 128 y - 110

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

f (x) = 16 - x^{2}, - 4 \leq x \leq 4

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

f (x) = x (16 - 47 + 2 x) (\frac{47}{2} - x)

What is the extreme f(x,y)=x^2+y^2-4x+17x-10y+2021 ?
The extreme f(x,y)=x^2+y^2-4x+17x-10y+2021 is Minimum(-13/2 ,5)