Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
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- scientia
- 2012-10-28 10:47:28
Let ; then when . So is decreasing for ; as , , i.e. .
- bob bundy
- 2012-10-27 21:31:57
Looks to me that y = x^(1/x) has a single maximum at x = e.
See graph and derivative graph.
Bob
- bobbym
- 2012-10-27 20:50:54
Hi;
e^e is not greater than π^π. That is not what I said. You did something wrong with the first step.
From here it is an ugly calculus problem.
- Harold
- 2012-10-27 20:47:54
You mean e^e is always bigger than pi^pi?but why?
- bobbym
- 2012-10-27 20:26:19
Hi Harold;
This one has been around for a long time. The standard answer starts with raising both sides to the power of
after that it is a maxima-minima problem.
- Harold
- 2012-10-27 19:46:42
What is the solution of this problem?and how is the problem solved-