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受欢迎的函数 >

extreme f(x)=2x-11ln(8x),2<= x<= 9

解答

极值点

f (x) = 2 x - 11 ln (8 x), 2 \leq x \leq 9

解答

极大值 (2, 4 - 44 ln (2)), 极小值 (\frac{11}{2}, 11 - 11 ln (44)), 极大值 (9, 18 - 11 ln (72))

求解步骤

找到临界点:

x = 2, x = \frac{11}{2}, x = 9

2 x - 11 ln (8 x), 2 \leq x \leq 9

的定义域

: 2 \leq x \leq 9

Find intervals:

递减

: 2 < x < \frac{11}{2},

递增

: \frac{11}{2} < x < 9

将极值点

x = 2

代入

2 x - 11 ln (8 x) \Rightarrow y = 4 - 44 ln (2)

极大值 (2, 4 - 44 ln (2))

将极值点

x = \frac{11}{2}

代入

2 x - 11 ln (8 x) \Rightarrow y = 11 - 11 ln (44)

极小值 (\frac{11}{2}, 11 - 11 ln (44))

将极值点

x = 9

代入

2 x - 11 ln (8 x) \Rightarrow y = 18 - 11 ln (72)

极大值 (9, 18 - 11 ln (72))

极大值 (2, 4 - 44 ln (2)), 极小值 (\frac{11}{2}, 11 - 11 ln (44)), 极大值 (9, 18 - 11 ln (72))

作图

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