[spursj911]

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

is this correct

[Swayum]

A point of intersection between what? And third derivative of what?

[Cities]

(Original post by spursj911)
if triple differenetiation not equal to 0
there is a point of intersection

is this correct

Point of inflexion I think you mean.

[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

[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'.

[Horizontal 8]

If I remember correctly, if doesn't equal 0 for 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.

[yodude888]

(Original post by 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.

[tommm]

(Original post by 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...

[Swayum]

(Original post by Horizontal 8)
If I remember correctly, if doesn't equal 0 for 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.

[Horizontal 8]

(Original post by 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

[Swayum]

(Original post by Horizontal 8)
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

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) .

[Cities]

(Original post by 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.

[Cities]

(Original post by 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.

[Horizontal 8]

Consider

This implies that at x = 0 =

However 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.

[Cities]

(Original post by Horizontal 8)
If I remember correctly, if doesn't equal 0 for 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.

[JonnyK81]

(Original post by 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!

[JonnyK81]

(Original post by yodude888)
Thank you. This information enables me to call person a "stupid third derivative" and feel superior.

LMFAO

[Cities]

(Original post by 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.

[Swayum]

(Original post by n1r4v)
Those wouldn't be stationary points however.

The first post said nothing about them being stationary points . I've read your other post though - thanks.

[Horizontal 8]

(Original post by 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. 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...