What is the extreme f(x,y)=x^2+5xy+y^2-2x+4y+5 ?

The extreme f(x,y)=x^2+5xy+y^2-2x+4y+5 is Saddle(-8/7 , 6/7)

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extreme f(x,y)=x^2+5xy+y^2-2x+4y+5

extreme points

f (x, y) = x^{2} + 5 x y + y^{2} - 2 x + 4 y + 5

Saddle (- \frac{8}{7}, \frac{6}{7})

Solution steps

Find the critical points:

(- \frac{8}{7}, \frac{6}{7})

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

D (x, y) = - 21

Check the sign of at each critical point

Check critical point

(- \frac{8}{7}, \frac{6}{7}) :

Saddle

Saddle (- \frac{8}{7}, \frac{6}{7})

f (x, y) = 9 x y + \frac{1000}{y} + \frac{1000}{x}

f (x) = - 2 x + 6 x^{\frac{2}{3}}, - 8 \leq x \leq 4.5

f (x) = 5 (x^{2} + 4)^{2} (x - 4)^{3}

f (x) = 4 x e^{- 2 x}

f (x) = 4 x^{3} - 39 x^{2} + 90 x - 6

What is the extreme f(x,y)=x^2+5xy+y^2-2x+4y+5 ?
The extreme f(x,y)=x^2+5xy+y^2-2x+4y+5 is Saddle(-8/7 , 6/7)