Question

Consider the function $f ( x )=\frac{ x }{2^{ x }}$ and $g ( x )=\max .\{ f ( t ): x \leq t \leq x +1\}$
If $f ( x )= k$ has 2 distinct real roots then range of $k$ is equal to

• A. $\left(0, \frac{1}{ e }\right)$
• B. $\left(0, \frac{1}{ e \ln 2}\right)$
• C. $\left(\frac{1}{ e \ln 2}, \infty\right)$
• D. $(-\infty, 0)$

Answer 1

Answer: (B)

Clearly, $f ( x )= k$ has two distinct roots for $k \in\left(0, \frac{1}{ e \ln 2}\right)$.