Forced Oscillation

★ 6/10functions Extrema algebra Completing the Square

Problem

Let $a > 0$ and $f(x) = ax^2 - x + 1$ . Suppose that on every closed interval of length $1$ there exist two points at which the values of $f$ differ by at least $1$ in absolute value. Find the minimum possible value of $a$ .

Answer

Solution

Difficulty	6/10
Topics	functions, Extrema, algebra, Completing the Square

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