What is the extreme f(x,y)=x^{-1}-64y^{-1}+xy ?

The extreme f(x,y)=x^{-1}-64y^{-1}+xy is Maximum(-1/4 ,16)

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extreme f(x,y)=x^{-1}-64y^{-1}+xy

extreme points

f (x, y) = x^{- 1} - 64 y^{- 1} + x y

Maximum (- \frac{1}{4}, 16)

Solution steps

Find the critical points:

(- \frac{1}{4}, 16)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{128}{y ^{3}}

D (x, y) = - \frac{256}{x ^{3} y ^{3}} - 1

Check the sign of at each critical point

Check critical point

(- \frac{1}{4}, 16) :

Maximum

Maximum (- \frac{1}{4}, 16)

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

x^{2} - y^{2} - 2 x + 4 y + 6

f (x) = ln (4 x^{2} + 18 y^{2} - 36)

f (x) = x^{3} + y^{3} - 15 x y

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

What is the extreme f(x,y)=x^{-1}-64y^{-1}+xy ?
The extreme f(x,y)=x^{-1}-64y^{-1}+xy is Maximum(-1/4 ,16)