What is the extreme 1/x+xy-8/y ?

The extreme 1/x+xy-8/y is Maximum(-1/2 ,4)

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extreme 1/x+xy-8/y

extreme points

\frac{1}{x} + x y - \frac{8}{y}

Maximum (- \frac{1}{2}, 4)

Solution steps

Find the critical points:

(- \frac{1}{2}, 4)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{16}{y ^{3}}

D (x, y) = - \frac{32}{x ^{3} y ^{3}} - 1

Check the sign of at each critical point

Check critical point

(- \frac{1}{2}, 4) :

Maximum

Maximum (- \frac{1}{2}, 4)

f (x, y) = y \cdot ln (x)

f (x) = x^{2} + x y + y^{2} - 37 y + 456

f (x) = 4 - 2 (x - 1)^{\frac{2}{3}}

f (x) = 3 x^{3} - 3 x

f (x) = 10 + x^{3} - \frac{9 x ^{2}}{2}