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受欢迎的函数 >

extreme f(x)=25x^2-x^3

解答

极值点

f (x) = 25 x^{2} - x^{3}

解答

极小值 (0, 0), 极大值 (\frac{50}{3}, \frac{62500}{27})

求解步骤

f^{'} (x) = 50 x - 3 x^{2}

Find intervals:

递减

: - \infty < x < 0,

递增

: 0 < x < \frac{50}{3},

递减

: \frac{50}{3} < x < \infty

将

x = 0

代入

25 x^{2} - x^{3} : 0

极小值 (0, 0)

将

x = \frac{50}{3}

代入

25 x^{2} - x^{3} : \frac{62500}{27}

极大值 (\frac{50}{3}, \frac{62500}{27})

极小值 (0, 0), 极大值 (\frac{50}{3}, \frac{62500}{27})

作图

流行的例子

extreme f(x)=4x^2-16x+20

e x t re m e f (x) = 4 x^{2} - 16 x + 20

extreme g(x)=-50x^2+400x+500

e x t re m e g (x) = - 50 x^{2} + 400 x + 500

extreme f(x)=4x+5y

e x t re m e f (x) = 4 x + 5 y

extreme x^{11}-3x^9+2

e x t re m e x^{11} - 3 x^{9} + 2

extreme x^3-2x^2-4x-4

e x t re m e x^{3} - 2 x^{2} - 4 x - 4