A Maximum at Zero

Problem

1. Prove that for $0 < x < 1$ ,

x - x^2 < \sin x < x.

Let $f(x) = \cos(ax) - \ln\left(1 - x^2\right)$ . If $x = 0$ is a local maximum point of $f(x)$ , find the range of possible values of $a$ .

Answer

Solution

Difficulty	7/10
Topics	Extrema, calculus, Monotonicity

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