Math Is Fun Forum

Annasophia

Guest

Finding points of inflexion?

For the curve y = (x)/(x^2 + 1)

Show the points of inflexion occur when x = 0, ±√3.

Help, please?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding points of inflexion?

Hi;

Were you able to differentiate that twice?

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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.

Annasophia

Guest

Re: Finding points of inflexion?

Kind of. I have the first derivative: (x^2 - 1)/(x^2 + 1)^2
But I don't know how to get to the second.
Thank you so much for replying, though.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding points of inflexion?

Hi Annasophia;

I am having some connection problems so I will be going on and off.

That is not correct for the first derivative.

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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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Finding points of inflexion?

hi Annasophia,

See graph below.

A point of inflexion is where the tangent to the curve crosses over the curve at that point.  So the gradient goes from (i) positive to maximum positive back to positive or (ii) negative to minimum negative to negative at that point.

I've put one tangent on the graph in red to show this happening.

So you need to find the points where the gradient function has a local maximum or minimum.  Your first derivative has a sign error so I'm thinking you knew it was a 'quotient' and just made a small slip.  As bobbym has said the correct answer is

Post back if you need help correcting your version.

This function needs to be differentiated again.  It's another quotient.

so

So when is this zero?

There are three values that make the numerator zero.  Those are the ones you want.

Bob

Last edited by Bob (2011-11-18 20:51:59)

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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

reconsideryouranswer

Member

Registered: 2011-05-11

Posts: 171

Re: Finding points of inflexion?

For the curve y = (x)/(x^2 + 1)

Show the points of

inflexion

occur when x = 0, ±√3.

I can't find a spelling for "inflexion."  You can use "inflection" instead.

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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding points of inflexion?

http://www.thefreedictionary.com/inflexion

I believe the OP is from Australia so the above spelling is probably being used.

There is a little bit more here:

http://en.wikipedia.org/wiki/Inflection

This url seems to suggest that it is an alternate spelling in the US.

http://www.thefreedictionary.com/inflection

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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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Finding points of inflexion?

hi reconsideryouranswer

We were obviously sad to lose you in 1776, but you, our American cousins, seem to getting along just fine, so that's ok.  You do have a bit of trouble from time to time with the language, but we're happy to forgive you that.  Newton invented the calculus well before that date so I think we have the prior claim on spelling!

Wiki and Dictionary.com both accept either.

My favourite (favorite) play on words showing the interesting usage on either side of the pond is:

The trunk is in the boot.  (Eng)

The boot is in the trunk. (Amer)

Vive la différence! 

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