Three Zeros With a Slope

★ 8/10functions Extrema calculus Monotonicity

Problem

Let $f(x) = \ln x - a\sqrt x$ .

1. Discuss the monotonicity of $f$ . 2. If some positive $k$ makes $g(x) = kx - 1 + f(x)$ have three zeros, find the range of $a$ .

Answer

Solution

Difficulty	8/10
Topics	functions, Extrema, calculus, Monotonicity

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