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受欢迎的函数 >

extreme f(x)=x^3-9x^2,-1<= x<= 7

解答

极值点

f (x) = x^{3} - 9 x^{2}, - 1 \leq x \leq 7

解答

极小值 (- 1, - 10), 极大值 (0, 0), 极小值 (6, - 108), 极大值 (7, - 98)

求解步骤

找到临界点:

x = - 1, x = 0, x = 6, x = 7

x^{3} - 9 x^{2}, - 1 \leq x \leq 7

的定义域

: - 1 \leq x \leq 7

Find intervals:

递增

: - 1 < x < 0,

递减

: 0 < x < 6,

递增

: 6 < x < 7

将极值点

x = - 1

代入

x^{3} - 9 x^{2} \Rightarrow y = - 10

极小值 (- 1, - 10)

将极值点

x = 0

代入

x^{3} - 9 x^{2} \Rightarrow y = 0

极大值 (0, 0)

将极值点

x = 6

代入

x^{3} - 9 x^{2} \Rightarrow y = - 108

极小值 (6, - 108)

将极值点

x = 7

代入

x^{3} - 9 x^{2} \Rightarrow y = - 98

极大值 (7, - 98)

极小值 (- 1, - 10), 极大值 (0, 0), 极小值 (6, - 108), 极大值 (7, - 98)

作图

流行的例子

extreme f(x,y)=sqrt(x^2+y^2+9)

e x t re m e f (x, y) = x^{2} + y^{2} + 9

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

extreme f(x)=2+9x+3x^2-x^3,-2<= x<= 6

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