課程名稱︰分析導論優一
課程性質︰數學系大二必修
課程教師︰王振男
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2014/11/04
考試時限（分鐘）：40
試題 :
1. (10%) Let h be a fixed positive number. Show that there is no function f
satisfying the following three conditions: f'(x) exists for x ≧ 0, f'(0) =
0, and f'(x) ≧ h for x > 0.
2. (10%) Let f be a real-valued function on [0, 1]. Assume that f(0) > 0, f(x)
≠ x for all x, and f(x) ≦ f(y) whenever x ≦ y. Let A = {x: f(x) > x}. Show
that sup A ∈ A and that f(1) > 1.