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受欢迎的函数 >

extreme f(x)= 1/(3x^3-9x+2)

解答

极值点

f (x) = \frac{1}{3 x ^{3} - 9 x + 2}

解答

极小值 (- 1, \frac{1}{8}), 极大值 (1, - \frac{1}{4})

求解步骤

找到临界点:

x = - 1, x = 1

\frac{1}{3 x ^{3} - 9 x + 2}

的定义域

: x < - 1.83398 \dots or - 1.83398 \dots < x < 0.22607 \dots or 0.22607 \dots < x < 1.60791 \dots or x > 1.60791 \dots

Find intervals:

递减

: - \infty < x < - 1.83398 \dots,

递减

: - 1.83398 \dots < x < - 1,

递增

: - 1 < x < 0.22607 \dots,

递增

: 0.22607 \dots < x < 1,

递减

: 1 < x < 1.60791 \dots,

递减

: 1.60791 \dots < x < \infty

将极值点

x = - 1

代入

\frac{1}{3 x ^{3} - 9 x + 2} \Rightarrow y = \frac{1}{8}

极小值 (- 1, \frac{1}{8})

将极值点

x = 1

代入

\frac{1}{3 x ^{3} - 9 x + 2} \Rightarrow y = - \frac{1}{4}

极大值 (1, - \frac{1}{4})

极小值 (- 1, \frac{1}{8}), 极大值 (1, - \frac{1}{4})

作图

流行的例子

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