What is the extreme f(x,y)=420x^2-80x+150y^2-75y+xy ?

The extreme f(x,y)=420x^2-80x+150y^2-75y+xy is Minimum(2175/22909 , 5720/22909)

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extreme f(x,y)=420x^2-80x+150y^2-75y+xy

extreme points

f (x, y) = 420 x^{2} - 80 x + 150 y^{2} - 75 y + x y

Minimum (\frac{2175}{22909}, \frac{5720}{22909})

Solution steps

Find the critical points:

(\frac{2175}{22909}, \frac{5720}{22909})

\frac{\partial ^{2} f}{\partial x ^{2}} = 300

D (x, y) = 251999

Check the sign of at each critical point

Check critical point

(\frac{2175}{22909}, \frac{5720}{22909}) :

Minimum

Minimum (\frac{2175}{22909}, \frac{5720}{22909})

f (x) = - \frac{2 x}{7 x ^{2} + 4}

P (x, y) = (x + 1) 2 - (y - 2) 2

f (z) = x^{2} + y^{2}

f (x) = 2 x^{3} - 3 x^{2} - 36 x + 54

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

What is the extreme f(x,y)=420x^2-80x+150y^2-75y+xy ?
The extreme f(x,y)=420x^2-80x+150y^2-75y+xy is Minimum(2175/22909 , 5720/22909)