A Minimal Count of Sine Points

★ 7/10trigonometry Extrema Absolute Value

Problem

Let $f(x)=\sin x$ . Suppose there exist $x_1,x_2,\dots,x_m$ with $0\leqslant x_1<x_2<\cdots<x_m\leqslant 6\pi$ such that

|f(x_1)-f(x_2)|+|f(x_2)-f(x_3)|+\cdots+|f(x_{m-1})-f(x_m)|=12

( $m\geqslant 2$ , $m\in\mathbb N^{*}$ ). Find the minimum value of $m$ .

Answer

Solution

Difficulty	7/10
Topics	trigonometry, Extrema, Absolute Value

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