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受欢迎的函数 >

extreme f(x)=(ln(x))/x ,1<= x<= 3

解答

极值点

f (x) = \frac{ln ( x )}{x}, 1 \leq x \leq 3

解答

极小值 (1, 0), 极大值 (e, \frac{1}{e}), 极小值 (3, \frac{ln ( 3 )}{3})

求解步骤

找到临界点:

x = 1, x = e, x = 3

\frac{ln ( x )}{x}, 1 \leq x \leq 3

的定义域

: 1 \leq x \leq 3

Find intervals:

递增

: 1 < x < e,

递减

: e < x < 3

将极值点

x = 1

代入

\frac{ln ( x )}{x} \Rightarrow y = 0

极小值 (1, 0)

将极值点

x = e

代入

\frac{ln ( x )}{x} \Rightarrow y = \frac{1}{e}

极大值 (e, \frac{1}{e})

将极值点

x = 3

代入

\frac{ln ( x )}{x} \Rightarrow y = \frac{ln ( 3 )}{3}

极小值 (3, \frac{ln ( 3 )}{3})

极小值 (1, 0), 极大值 (e, \frac{1}{e}), 极小值 (3, \frac{ln ( 3 )}{3})

作图

流行的例子

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