# Don't undertstand what they are asking

## Homework Statement

The goal of this problem is to use the Intermediate Value Theorem to prove that there exists a positive number c which is the fifth root of 2.

Another way of expressing this is that we would like to find a positive root \,c of the continuous function f(x) = x^5 - ??? .
Note: Fill in the box with an appropriate constant to complete the definition of the function f(x).

## The Attempt at a Solution

I tried 32, 1/32, which I thought they were just asking for 2^5? But I guess not.. I understand what the intermediate value theorem is, but not in the context of what they are asking.

pasmith
Homework Helper

## Homework Statement

The goal of this problem is to use the Intermediate Value Theorem to prove that there exists a positive number c which is the fifth root of 2.

Another way of expressing this is that we would like to find a positive root \,c of the continuous function f(x) = x^5 - ??? .
Note: Fill in the box with an appropriate constant to complete the definition of the function f(x).

## The Attempt at a Solution

I tried 32, 1/32, which I thought they were just asking for 2^5? But I guess not.. I understand what the intermediate value theorem is, but not in the context of what they are asking.

You need to have f(x) = 0 when $x = 2^{1/5}$, not when $x = 2^5$.

The root of x^5-C is when x^5-C=0. You want to find some constant C such that the root is the fifth root of 2.

Oh got it, 2^1/5^5 = 2 so c = 2 thanks!

Oh got it, 2^1/5^5 = 2 so c = 2 thanks!

C=2, but I don't get your logic.

Ray Vickson