The Smallest Maximum

★ 6/10functions trigonometry Extrema Substitution Completing the Square

Problem

Let $f(x) = (a + \sin x)(a + \cos x)$ , and let $g(a)$ denote the maximum value of $f(x)$ as $x$ ranges over the reals. Find $g(a)$ , and find the minimum value of $g(a)$ .

Answer

Solution

Difficulty	6/10
Topics	functions, trigonometry, Extrema, Substitution, Completing the Square

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