What is the extreme f(x,y)=(8460)/x+(8460)/y+5xy ?

The extreme f(x,y)=(8460)/x+(8460)/y+5xy is Minimum(\sqrt[3]{1692},6^{2/3}\sqrt[3]{47})

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extreme f(x,y)=(8460)/x+(8460)/y+5xy

extreme points

f (x, y) = \frac{8460}{x} + \frac{8460}{y} + 5 x y

Solution steps

Find the critical points:

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{16920}{y ^{3}}

D (x, y) = \frac{286286400}{x ^{3} y ^{3}} - 25

Check the sign of at each critical point

Check critical point

Minimum

f (x) = (85 - 0.05 x) - (600 + 35 x)

f (x) = 4 x^{2} - 24 x + 400

f (x, y) = - 5 x^{2} - 6 y^{2} + 5 x - 12 y + 5

f (x) = - 9 + 2 x - x^{2}

f (x, y) = 2 x^{2} + 2 y^{2} - 16 x + 16 y

What is the extreme f(x,y)=(8460)/x+(8460)/y+5xy ?
The extreme f(x,y)=(8460)/x+(8460)/y+5xy is Minimum(\sqrt[3]{1692},6^{2/3}\sqrt[3]{47})