Math Is Fun Forum

Harold

Guest

Inequality with pi and e

What is the solution of this problem?and how is the problem solved-

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Inequality with pi and e

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Harold

Guest

Re: Inequality with pi and e

You mean e^e is always bigger than pi^pi?but why?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Inequality with pi and e

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.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,646

Re: Inequality with pi and e

Looks to me that y = x^(1/x) has a single maximum at x = e.

See graph and derivative graph.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

scientia

Member

Registered: 2009-11-13

Posts: 224

Re: Inequality with pi and e

Let

; then

when

. So

is decreasing for

; as

,

, i.e.

.