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受欢迎的函数 >

extreme f(x)=x^4-6x^2+2x+3

解答

极值点

f (x) = x^{4} - 6 x^{2} + 2 x + 3

解答

极小值 (- 1.81003 \dots, - 9.54376 \dots), 极大值 (0.16825 \dots, 3.16745 \dots), 极小值 (1.64178 \dots, - 2.62368 \dots)

求解步骤

找到临界点:

x = - 1.81003 \dots, x \approx 0.16825 \dots, x \approx 1.64178 \dots

x^{4} - 6 x^{2} + 2 x + 3

的定义域

: - \infty < x < \infty

Find intervals:

递减

: - \infty < x < - 1.81003 \dots,

递增

: - 1.81003 \dots < x < 0.16825 \dots,

递减

: 0.16825 \dots < x < 1.64178 \dots,

递增

: 1.64178 \dots < x < \infty

将极值点

x = - 1.81003 \dots

代入

x^{4} - 6 x^{2} + 2 x + 3 \Rightarrow y = - 9.54376 \dots

极小值 (- 1.81003 \dots, - 9.54376 \dots)

将极值点

x = 0.16825 \dots

代入

x^{4} - 6 x^{2} + 2 x + 3 \Rightarrow y = 3.16745 \dots

极大值 (0.16825 \dots, 3.16745 \dots)

将极值点

x = 1.64178 \dots

代入

x^{4} - 6 x^{2} + 2 x + 3 \Rightarrow y = - 2.62368 \dots

极小值 (1.64178 \dots, - 2.62368 \dots)

极小值 (- 1.81003 \dots, - 9.54376 \dots), 极大值 (0.16825 \dots, 3.16745 \dots), 极小值 (1.64178 \dots, - 2.62368 \dots)

作图

流行的例子

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