The maximum value of (1/x)ˣ is:

The maximum value of (1/x)ˣ is:

• A. e^(1/e)
• B. e^e
• C. e^(−e)
• D. e^(−1/e)

Answer: A) e^(1/e)

Explanation: Let y = (1/x)ˣ = e^(x ln(1/x)) = e^(−x ln x). Maximize y equivalent to minimize x ln x. g(x) = x ln x. g'(x) = ln x + 1 = 0 → x = 1/e. g(1/e) = (1/e)(−1) = −1/e. Max y = e^(−(−1/e)) = e^(1/e).