Question

problem inside! :)

Answer 1

For which positive integer \[n\] is \[n ^{\frac{ 1 }{ n }}\] largest?

x=_______

Answer 2

sorry, i meant n=______

Answer 3

@iheartfood, which do you believe is correct?

Answer 4

What value of \(n\) do you believe is correct

Answer 5

and sorry it's not too clear, but that's n^(1/n)

:)

and not too sure.... but i'm thinking 1 ?

1^(1/1) = 1 ? :/

is that right?

Answer 6

but not very sure about how to find the value mathematically? :/

Answer 7

Well, but 2^(1/2) = 1.41421 > 1

Answer 8

ohhhh :(

darn then yeah, i'm not sure how to go about solving this :/

what would be the first step?

Answer 9

Trying different values of n until you realize something. I recommend starting with n = 1, then n = 2 and so on

Answer 10

okay

so n=1 you get 1
n=2 you get 1.41
n=3 you get 1.44
n=4 you get 1.41
n=5 you get 1.38

hmm, it goes back and forth? :/

Answer 11

is this calculus or number theory ?
you sure it is asking for "integer" ?

Answer 12

@iheartfood, you give up too easily

Answer 13

It doesn't go "back and forth". It reaches a peak, then declines from there.

Answer 14

Maybe you should try graphing

\(y = x^{1/x}\)

Answer 15

calculus :)

so n=1 you get 1
n=2 you get 1.41
n=3 you get 1.44
n=4 you get 1.41
n=5 you get 1.38
and then

n=6 you get 1.35
n=7 you get 1.32
n=8 you get 1.30

so it hits its peak at n=3? :/

Answer 16

Yes, correct.

Answer 17

You can use calculus to figure it out

Answer 18

ahh okay yay! thank you! :D