MathDB

5

Part of 1998 Israel National Olympiad

Problems(1)

|ax+b-\sqrt{x}| \le 1/24 for 1 <= x <=4

Source: Israel Joseph Gillis Mathematical Olympiad 1998 p5

2/16/2020
(a) Find two real numebrs a,ba,b such that ∣ax+b−x∣≤124|ax+b-\sqrt{x}| \le \frac{1}{24} for 1≤x≤41 \le x \le 4. (b) Prove that the constant 124\frac{1}{24} cannot be replaced by a smaller one.
inequalitiesalgebra