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受欢迎的函数 >

extreme (x-7)(x-5)^2(x-3)(x-1)

解答

极值点

(x - 7) (x - 5)^{2} (x - 3) (x - 1)

解答

极大值 (1.65442 \dots, 52.68703 \dots), 极小值 (3.68776 \dots, - 10.54328 \dots), 极大值 (5, 0), 极小值 (6.45780 \dots, - 21.74567 \dots)

求解步骤

找到临界点:

x \approx 1.65442 \dots, x \approx 3.68776 \dots, x = 5, x = 6.45780 \dots

(x - 7) (x - 5)^{2} (x - 3) (x - 1)

的定义域

: - \infty < x < \infty

Find intervals:

递增

: - \infty < x < 1.65442 \dots,

递减

: 1.65442 \dots < x < 3.68776 \dots,

递增

: 3.68776 \dots < x < 5,

递减

: 5 < x < 6.45780 \dots,

递增

: 6.45780 \dots < x < \infty

将极值点

x = 1.65442 \dots

代入

(x - 7) (x - 5)^{2} (x - 3) (x - 1) \Rightarrow y = 52.68703 \dots

极大值 (1.65442 \dots, 52.68703 \dots)

将极值点

x = 3.68776 \dots

代入

(x - 7) (x - 5)^{2} (x - 3) (x - 1) \Rightarrow y = - 10.54328 \dots

极小值 (3.68776 \dots, - 10.54328 \dots)

将极值点

x = 5

代入

(x - 7) (x - 5)^{2} (x - 3) (x - 1) \Rightarrow y = 0

极大值 (5, 0)

将极值点

x = 6.45780 \dots

代入

(x - 7) (x - 5)^{2} (x - 3) (x - 1) \Rightarrow y = - 21.74567 \dots

极小值 (6.45780 \dots, - 21.74567 \dots)

极大值 (1.65442 \dots, 52.68703 \dots), 极小值 (3.68776 \dots, - 10.54328 \dots), 极大值 (5, 0), 极小值 (6.45780 \dots, - 21.74567 \dots)

作图

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