Nonnegative After Zero

Problem

Let f(x)=(1ax)ln(1+x)xf(x) = (1 - ax)\ln(1 + x) - x.

1. When a=2a = -2, find the extreme values of f(x)f(x). 2. If f(x)0f(x) \geqslant 0 for all x0x \geqslant 0, find the range of possible values of aa.

Answer

Solution

Difficulty7/10
Topicscalculus, Convexity, Monotonicity, inequality

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