Sliding a Parabola Under a Line

★ 7/10functions Quadratic Equations Completing the Square inequality

Problem

Let $f(x) = x^2 + 2x + 1$ . Suppose there is a real $t$ such that

f(x + t) \leqslant x \qquad \text{for all } x \in [1, m].

Find the maximum possible value of the real number $m$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Quadratic Equations, Completing the Square, inequality

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