A Local Max at the Origin

★ 6/10functions Extrema calculus Monotonicity

Problem

Let $f(x) = \mathrm{e}^x - x - ax\ln(x+1) - 1$ .

1. If $a = 0$ , find the minimum value of $f(x)$ . 2. If $f(x)$ has a local maximum at $x = 0$ , find the range of possible values of $a$ .

Answer

Solution

Difficulty	6/10
Topics	functions, Extrema, calculus, Monotonicity

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