Counting Zeros on an Interval

★ 6/10functions calculus Monotonicity Casework Discriminant

Problem

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

1. For $a \geqslant 0$ , discuss the monotonicity of $f(x)$ . 2. Find the number of zeros of $f(x)$ on $[0, 1]$ .

Answer

Solution

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

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