extreme f(x)=x^3-ax^2

解答

极值点

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

{a < 0 : 极小值 (0, 0), a > 0 : 极大值 (0, 0)}

求解步骤

找到临界点:

x = 0, x = \frac{2 a}{3}

f^{''} (x) = 6 x - 2 a

检查

f^{''} (x) = 6 x - 2 a

在每个临界点处的符号

检查临界点

x = 0 : {a < 0 : 极小值 (0, 0), a > 0 : 极大值 (0, 0)}

{a < 0 : 极小值 (0, 0), a > 0 : 极大值 (0, 0)}

e x t re m e f (x) = 3 x^{2} + 4 y^{3} - 12 x y + 37

e x t re m e f (x) = 15 x + 18 y - 2 x^{2} + 2 x y + 3 y^{2}

e x t re m e f (x, y) = x^{3} - 12 x + y^{2} + 6 y + 14

e x t re m e f (x) = x^{- 7} ln (x)

e x t re m e y = \frac{5 x ^{2}}{( x - 4 ) ^{2}}