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受欢迎的函数 >

extreme f(x)=-x^6-3x^3+x+1

解答

极值点

f (x) = - x^{6} - 3 x^{3} + x + 1

解答

极大值 (- 1.10915 \dots, 2.12248 \dots), 极小值 (- 0.33769 \dots, 0.77635 \dots), 极大值 (0.32943 \dots, 1.22089 \dots)

求解步骤

找到临界点:

x \approx - 1.10915 \dots, x \approx - 0.33769 \dots, x \approx 0.32943 \dots

- x^{6} - 3 x^{3} + x + 1

的定义域

: - \infty < x < \infty

Find intervals:

递增

: - \infty < x < - 1.10915 \dots,

递减

: - 1.10915 \dots < x < - 0.33769 \dots,

递增

: - 0.33769 \dots < x < 0.32943 \dots,

递减

: 0.32943 \dots < x < \infty

将极值点

x = - 1.10915 \dots

代入

- x^{6} - 3 x^{3} + x + 1 \Rightarrow y = 2.12248 \dots

极大值 (- 1.10915 \dots, 2.12248 \dots)

将极值点

x = - 0.33769 \dots

代入

- x^{6} - 3 x^{3} + x + 1 \Rightarrow y = 0.77635 \dots

极小值 (- 0.33769 \dots, 0.77635 \dots)

将极值点

x = 0.32943 \dots

代入

- x^{6} - 3 x^{3} + x + 1 \Rightarrow y = 1.22089 \dots

极大值 (0.32943 \dots, 1.22089 \dots)

极大值 (- 1.10915 \dots, 2.12248 \dots), 极小值 (- 0.33769 \dots, 0.77635 \dots), 极大值 (0.32943 \dots, 1.22089 \dots)

作图

流行的例子

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