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

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

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

extreme points

f (x, y) = 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, y) = 3 x + y

f (t) = (1 + 2 t - 3 t^{2} + 4 t^{3}) u (t - 2)

f (x) = 3 x^{3} - 9 x^{2}

f (x) = - \frac{2}{5} x^{5} + 5 x^{4} - 16 x^{3} - 19

f (x) = - 0.2 x^{3} + 969 x - 870

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