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