Two Zeros of a Mixed Function

★ 6/10functions calculus Monotonicity Casework

Problem

Let $f(x) = (x-2)\mathrm{e}^x + a(x-1)^2$ .

1. Discuss the monotonicity of $f(x)$ . 2. If $f(x)$ has two zeros, find the range of possible values of the real number $a$ .

Answer

Solution

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

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