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

解答

极值点

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

极大值 (\frac{1}{2}, 1)

求解步骤

找到临界点:

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

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

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

检查在每个临界点处的符号

检查临界点

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

极大值

极大值 (\frac{1}{2}, 1)

e x t re m e f (x, y) = 3 x + y

e x t re m e f (t) = (1 + 2 t - 3 t^{2} + 4 t^{3}) u (t - 2)

e x t re m e f (x) = 3 x^{3} - 9 x^{2}

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

e x t re m e f (x) = x^{4} + x^{3} - 4 x^{2} - 4 x