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

The extreme f(x,y)=2x^2+3xy+4y^2-2x+10y is Minimum(2,-2)

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

extreme points

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

Minimum (2, - 2)

Solution steps

Find the critical points:

(2, - 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = 8

D (x, y) = 23

Check the sign of at each critical point

Check critical point

(2, - 2) :

Minimum

Minimum (2, - 2)

2 x^{3} - 24 x + 1

f (x) = x^{7} e^{2 x} + 2

f (x) = x^{3} + 12 x y + y^{4}

f (x) = 3 x - 5 ln (4 x)

f (x, y) = - \frac{4}{x ^{2}}, 0.5 \leq x \leq 4

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