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

The extreme f(x,y)=xy+x^2+y^2-x+y+17 is Minimum(1,-1)

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extreme f(x,y)=xy+x^2+y^2-x+y+17

extreme points

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

Minimum (1, - 1)

Solution steps

Find the critical points:

(1, - 1)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(1, - 1) :

Minimum

Minimum (1, - 1)

f (x) = 2 x^{3} - 3 x^{2} - 12 x + 1, - 4 \leq x \leq 5

f (x) = 4 x - 12 x^{\frac{1}{3}}

f (x) = 3 x + 2 cos (x)

f (t) = \frac{t}{t - 4}

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

What is the extreme f(x,y)=xy+x^2+y^2-x+y+17 ?
The extreme f(x,y)=xy+x^2+y^2-x+y+17 is Minimum(1,-1)