Question

(本小題滿分10分)
判斷（x∈[0，3]）的單調性，并證明你的結論．

Answer 1

f(x)在[0，3]上遞增，證明略。

解：，∴f(x)在[0，3]上遞增，·········································· 2分
證明：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] 上遞增．······················································· 10分