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

Source: Israel Joseph Gillis Mathematical Olympiad 1998 p5

February 16, 2020
inequalitiesalgebra

Problem Statement

(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.
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