Tangent at the Origin

★ 7/10functions Extrema calculus Monotonicity

Problem

The graph of $f(x) = \mathrm{e}^x - ax\sin x - bx + c$ is tangent to the $x$ -axis at the origin.

1. Find $b$ and $c$ . 2. If $f(x)$ has a unique zero in $(0, \pi)$ , find the range of possible values of the real number $a$ .

Answer

Solution

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

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