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d3y/dx3

if triple differenetiation not equal to 0
there is a point of intersection

is this correct

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Reply 1
A point of intersection between what? And third derivative of what?
Reply 2
spursj911
if triple differenetiation not equal to 0
there is a point of intersection

is this correct


Point of inflexion I think you mean.
Reply 3
If inflexion, then no. Consider y = x^5, which does have its third derivative = 0 at x = 0. And futhermore, consider

y = x^4
dy/dx = 4x^3
d^2y/dx^2 = 12x^2
d^3y/dx^3 = 24x

x = 1 ==> d^3y/dx^3 = 24, so according to your theory, there is a point of inflexion there.

x = 2 ==> d^3y/dx^3 = 48, so according to your theory, there is a point of inflexion there.

etc
Reply 4
No. The third derivative holds no real significance in the Mathematics of graphing functions.
On the other hand, in bungee jumping and space travel it is of paramount importance and is known as 'jerk'.
If I remember correctly, if dnydxn \frac{d^ny}{dx^n} doesn't equal 0 for n>2,nϵN n>2, n\epsilon N then this implies a point of inflexion.
Not 100% sure though cuz we did this a couple of months ago..

EDIT sorry if we weren't specific enough but this is given that dy/dx = 0 at the point and so does d^2/dx^2.
Reply 6
v-zero
No. The third derivative holds no real significance in the Mathematics of graphing functions.
On the other hand, in bungee jumping and space travel it is of paramount importance and is known as 'jerk'.


Thank you. This information enables me to call person a "stupid third derivative" and feel superior.
Reply 7
yodude888
Thank you. This information enables me to call person a "stupid third derivative" and feel superior.


Haha, I've done this before. I think I said "with respect to time" on the end of it, as well...
Reply 8
8 Horizontal
If I remember correctly, if dnydxn \frac{d^ny}{dx^n} doesn't equal 0 for n>2,nϵN n>2, n\epsilon N then this implies a point of inflexion.
Not 100% sure though cuz we did this a couple of months ago..

EDIT sorry if we weren't specific enough but this is given that dy/dx = 0 at the point and so does d^2/dx^2.


Counter-example: y = x^5, where dy/dx = d^2y/dx^2 = d^3/dx^3 = 0 at x = 0 and yet there's a point of inflexion.
Swayum
Counter-example: y = x^5, where dy/dx = d^2y/dx^2 = d^3/dx^3 = 0 at x = 0 and yet there's a point of inflexion.



that implies that there could be a point of inflexion. It doesn't imply that there is no point of inflexion see what I mean?

If it doesnt equal 0 there is a point of inflexion it has nothing to say about when it equals 0 :smile:
Reply 10
8 Horizontal
that implies that there could be a point of inflexion. It doesn't imply that there is no point of inflexion see what I mean?

If it doesnt equal 0 there is a point of inflexion it has nothing to say about when it equals 0 :smile:


Ok, fair enough. I've never heard of that though so I'm not yet willing to accept it (and don't have time to think of counter examples) :p:.
Reply 11
Swayum
Counter-example: y = x^5, where dy/dx = d^2y/dx^2 = d^3/dx^3 = 0 at x = 0 and yet there's a point of inflexion.


f'''(x) =/= 0 isn't a necessary condition for having a point of inflexion, but a sufficient one.

Although if f'''(x) = 0, I'm not sure how you would go about determining what type of stationary point it is.
Reply 12
Swayum
If inflexion, then no. Consider y = x^5, which does have its third derivative = 0 at x = 0. And futhermore, consider

y = x^4
dy/dx = 4x^3
d^2y/dx^2 = 12x^2
d^3y/dx^3 = 24x

x = 1 ==> d^3y/dx^3 = 24, so according to your theory, there is a point of inflexion there.

x = 2 ==> d^3y/dx^3 = 48, so according to your theory, there is a point of inflexion there.

etc


Those wouldn't be stationary points however.
Consider y=5x612x5 y = 5x^6-12x^5

This implies that at x = 0 dydx \frac{dy}{dx} = d2ydx2\frac{d^2y}{dx^2} =d3ydx3= \frac{d^3y}{dx^3}=d4ydx4=0= \frac{d^4y}{dx^4} = 0

However d5ydx5=1440 \frac{d^5y}{dx^5} = -1440 at x=0 therefore there is a point of inflexion.

EDIT: sorry about my poor latesx skills but I think I've solved it now.
Reply 14
8 Horizontal
If I remember correctly, if dnydxn \frac{d^ny}{dx^n} doesn't equal 0 for n>2,nϵN n>2, n\epsilon N then this implies a point of inflexion.
Not 100% sure though cuz we did this a couple of months ago..

EDIT sorry if we weren't specific enough but this is given that dy/dx = 0 at the point and so does d^2/dx^2.


There may be a stipulation that n must be odd.

Take y=x^6 or x^4 at x=0 for instance.
Reply 15
v-zero
No. The third derivative holds no real significance in the Mathematics of graphing functions.
On the other hand, in bungee jumping and space travel it is of paramount importance and is known as 'jerk'.


Is it really? Thats Fascinating! I was going to say something funny like "it takes one to know one" but then I realised I would be a jerk if I did that!
Reply 16
yodude888
Thank you. This information enables me to call person a "stupid third derivative" and feel superior.


LMFAO
Reply 17
v-zero
No. The third derivative holds no real significance in the Mathematics of graphing functions.
On the other hand, in bungee jumping and space travel it is of paramount importance and is known as 'jerk'.


Wikipedia demanded me to tell you that higher order derivatives are called snap, crackle and pop.
Reply 18
n1r4v
Those wouldn't be stationary points however.


The first post said nothing about them being stationary points :p:. I've read your other post though - thanks.
n1r4v
There may be a stipulation that n must be odd.

Take y=x^6 or x^4 at x=0 for instance.


Sorry, I don't see what you mean:s-smilie:. Those are minimum points at x=0, and d^ny/dx^n is equal to 0 for all natural n.. Implying that there could be a point of inflexion but we know there isn't...