(本小题满分10分) 判断（x∈[0，3]）的单调性，并证明你的结论．

题型：解答题难度：简单来源：不详

(本小题满分10分)
判断（x∈[0，3]）的单调性，并证明你的结论．

答案

f(x)在[0，3]上递增，证明略。

解析

解：，∴f(x)在[0，3]上递增，·········································· 2分
证明：f(x+h)-f(x)=，······················· 6分
∵x + h，x∈[0，3]，
∴x + h + 1 > 0，x + 1 > 0，························································ 8分
又∵h > 0，
∴f ( x + h)- f (x)> 0，········································· 9分
∴f (x) 在[0，3] 上递增．······················································· 10分