Question

(本小题满分10分)

判断（x∈[0，3]）的单调性，并证明你的结论．

Answer

f(x)在[0，3]上递增，证明略。

【解析】【解析】
，∴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