What is the extreme f(x)=ln(xy-6) ?

The extreme f(x)=ln(xy-6) is Saddle(0,0)

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extreme f(x)=ln(xy-6)

extreme points

f (x) = ln (x y - 6)

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{x ^{2}}{( x y - 6 ) ^{2}}

D (x, y) = \frac{x y + 6}{( - 6 + x y ) ^{3}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = e^{4 x} + e^{- x}

f (x, y) = 3 x^{2} + 2 y^{2} - 18 x + 16 y + 7

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

y = \frac{- 3 x}{x ^{2} + 2}

f (x) = 2 π r^{2} + \frac{1500}{r}