FUNCTION_MANY#extreme f(x)=25x-25xe^{-y}-50y-x^2

解答

极值点

f (x) = 25 x - 25 x e^{- y} - 50 y - x^{2}

鞍点 (\frac{5}{2}, - ln (\frac{4}{5})), 极大值 (10, ln (5))

求解步骤

找到临界点:

(\frac{5}{2}, - ln (\frac{4}{5})), (10, ln (5))

\frac{\partial ^{2} f}{\partial x ^{2}} = - 25 e^{- y} x

D (x, y) = 50 e^{- y} x - 625 e^{- 2 y}

检查在每个临界点处的符号

检查临界点

(\frac{5}{2}, - ln (\frac{4}{5})) :

鞍点

检查临界点

(10, ln (5)) :

极大值

鞍点 (\frac{5}{2}, - ln (\frac{4}{5})), 极大值 (10, ln (5))

e x t re m e f (x) = csc^{2} (x) - \frac{2}{3} cot (x)

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

e x t re m e f (x) = 3 - x

e x t re m e f (x) = x^{2} - 14 x + 44

e x t re m e \frac{x}{x ^{2} + 100}