Two Solutions with a Parameter

★ 7/10functions calculus Substitution Monotonicity Casework

Problem

Let

f(x) = \frac{\mathrm{e}^x}{x} - 4, \qquad g(x) = a - \frac{4ax}{\mathrm{e}^x}.

If the equation $f(x) = g(x)$ has exactly two real solutions on $(0, +\infty)$ , find the range of possible values of the real number $a$ .

Answer

Solution

Difficulty	7/10
Topics	functions, calculus, Substitution, Monotonicity, Casework

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