What is the extreme f(x,y)=x^3+y^2-4xy+17x-10y+2021 ?

The extreme f(x,y)=x^3+y^2-4xy+17x-10y+2021 is Minimum(3,11),Saddle(-1/3 , 13/3)

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extreme f(x,y)=x^3+y^2-4xy+17x-10y+2021

extreme points

f (x, y) = x^{3} + y^{2} - 4 x y + 17 x - 10 y + 2021

Minimum (3, 11), Saddle (- \frac{1}{3}, \frac{13}{3})

Solution steps

Find the critical points:

(3, 11), (- \frac{1}{3}, \frac{13}{3})

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

D (x, y) = 12 x - 16

Check the sign of at each critical point

Check critical point

(3, 11) :

Minimum

Check critical point

(- \frac{1}{3}, \frac{13}{3}) :

Saddle

Minimum (3, 11), Saddle (- \frac{1}{3}, \frac{13}{3})

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

y = 7 x + 7 sin (x)

f (x) = 4 x^{2} + 3 x^{2} - 6 x + 1

\frac{4 x + 13}{- 2 x - 6}

y = x^{4} - 12 x^{3} + 48 x^{2} - 64 x

What is the extreme f(x,y)=x^3+y^2-4xy+17x-10y+2021 ?
The extreme f(x,y)=x^3+y^2-4xy+17x-10y+2021 is Minimum(3,11),Saddle(-1/3 , 13/3)