What is the extreme f(x)=2ln(x)+ln(y)-4x-y ?

The extreme f(x)=2ln(x)+ln(y)-4x-y is Maximum(1/2 ,1)

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extreme f(x)=2ln(x)+ln(y)-4x-y

extreme points

f (x) = 2 ln (x) + ln (y) - 4 x - y

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

Solution steps

Find the critical points:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{1}{y ^{2}}

D (x, y) = \frac{2}{x ^{2} y ^{2}}

Check the sign of at each critical point

Check critical point

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

Maximum

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

f (x) = \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 2 x + 8

f (x) = - 3 x^{2} + 7 x - y^{2} + 4 y + 7

f (x) = 20 e^{- 0.1 \cdot 10}

f (x) = ∣ x y ∣

f (x) = - 2 x^{2} + 12 - 25

What is the extreme f(x)=2ln(x)+ln(y)-4x-y ?
The extreme f(x)=2ln(x)+ln(y)-4x-y is Maximum(1/2 ,1)