A Sliding-Window Maximum

★ 7/10functions trigonometry Extrema Casework

Problem

For a closed interval $I$ , let $M_I$ denote the maximum value of the function $y=\sin x$ on $I$ . Suppose a positive number $a$ satisfies

M_{[0,a]}=2M_{[a,2a]}.

Find $a$ .

Answer

Solution

Difficulty	7/10
Topics	functions, trigonometry, Extrema, Casework

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