# Homework Help: Finding the point of inflection of the integral of (sin(x))/x

1. Sep 28, 2010

### 312213

1. The problem statement, all variables and given/known data
Find the coordinates of the first inflection point to the right of the origin.

2. Relevant equations

3. The attempt at a solution
I know that the inflection point would equal zero for the second derivative of a function and that the second derivative of this function is (xcosx-sinx)/x².
(xcosx-sinx)/x² = 0
(xcosx-sinx) = 0
xcosx = sinx
x = tanx

I'm not sure what to do after this or if the steps were taken incorrectly.

2. Sep 28, 2010

### jackmell

I don't see what's wrong with that unless you don't know how to then find them numerically.

3. Sep 28, 2010

### 312213

I know that I can find the approximate number but I don't know where to go next to find the exact value of x for the first inflection point.

I don't know what steps to take next to isolate x in one side and to have one x.

4. Sep 28, 2010

### Inferior89

5. Sep 28, 2010

### 312213

So then an acceptable answer would be (tan(x),Si(tan(x))?

6. Sep 28, 2010

### Inferior89

The points of inflexions are when $$\tan x = x$$ as you said. This equation have an infinite number of solutions.

I don't really understand what you mean with $$( \tan(x), Si(\tan(x) )$$.
One point of inflexion would be for example $$( x_1 , Si(x_1))$$ where $$x_1$$ is defined to be the first positive solution to the equation $$\tan x = x$$

7. Sep 28, 2010

### 312213

I see and understand now. Thanks for the help.

8. Sep 28, 2010

### Bohrok

[EDIT] Thanks Inferior89

[STRIKE]Actually that's just the first derivative, not the second.
[/STRIKE]
If you want to [STRIKE]consider the values that give the extreme points of sinx/x where you would actually[/STRIKE] solve x = tanx, you might want to take a look here on the second page.
http://press.princeton.edu/books/maor/chapter_10.pdf [Broken]
Very interesting.

Last edited by a moderator: May 4, 2017
9. Sep 28, 2010

### Inferior89

He is finding the second derivative of Si(x) not sin(x)/x.

Last edited by a moderator: May 4, 2017