Counting Zeros with a Parameter

★ 7/10Extrema calculus Monotonicity Estimation

Problem

Let $a>0$ and

f(x)=\ln(2x+1)+2ax-4a\mathrm e^x+4.

1. For $a=1$ , find the maximum value of $f(x)$ . 2. Determine the number of zeros of $f(x)$ , and justify your answer.

Answer

Solution

Difficulty	7/10
Topics	Extrema, calculus, Monotonicity, Estimation

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