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# Difference between Turning point and Stationary point

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1. (Original post by Crystalclearmagic)
They're used rather interchangeably in maths even at A level - no?

If they're two different things, then Edexcel has misled me for 2 years then... :/
This is frequently mis-taught at A level. Another wrong idea is that 'if d2y/dx^2 = 0 then you have a point of inflection'. It's true you may have, but on the simple case of y = x^4 the second derivative is zero at the stationary point at the origin. But it's clearly a minimum.
2. (Original post by ian.slater)
This is frequently mis-taught at A level. Another wrong idea is that 'if d2y/dx^2 = 0 then you have a point of inflection'. It's true you may have, but on the simple case of y = x^4 the second derivative is zero at the stationary point at the origin. But it's clearly a minimum.
If d2y/dx2=0 and d3y/dx3 not= 0 then its a point of inflection, right?
3. (Original post by TenOfThem)
Sorry

My question related to the fact that y=x^3-x has no such point at (0,0)
Unless I've made some silly mistake, it does. All cubics have rotational symmetry about their point of inflection, which in this case is at (0,0). This curve switches from curving downwards for x<0 to curving upwards for x>0. The circle of curvature swaps sides at that point. But it's not a stationary point and is therefore a good example for me to use.
4. (Original post by raheem94)
If d2y/dx2=0 and d3y/dx3 not= 0 then its a point of inflection, right?
I think so ... that way the gradient has either a local maximum or minimum, which causes the curvature to 'flip' whether or not it's a stationary point.
5. (Original post by ian.slater)
I think so ... that way the gradient has either a local maximum or minimum, which causes the curvature to 'flip' whether or not it's a stationary point.
Thanks
6. THat just proves tenofthem right

Points of inflections are stationary points.
7. (Original post by TheGrinningSkull)
THat just proves tenofthem right

Points of inflections are stationary points.
It is written Inflection points may be stationary points

It is written 'may'?

8. (Original post by raheem94)
It is written Inflection points may be stationary points

It is written 'may'?

Thanks, I needed an example because it said may yet it offered no examples.

I still can't picture it visually though :s
9. (Original post by TheGrinningSkull)
Thanks, I needed an example because it said may yet it offered no examples.

I still can't picture it visually though :s
http://www.wolframalpha.com/input/?i=x^3+-x
10. (Original post by verello12)
Is there a Difference between Turning point and Stationary point or are they the same thing.
Im doing C3 OCR MEI btw.
I know how to find turning point of a curve you do dy/dx=0 to get x then substiute x in curve equation to get y

If a question asked you to find stationary point of a curve would you just do the same thing?
Yeah, but if it does equal o, and it could be a point of inflection to check, you put in the value of x in the original equation then x+0.1 and x-0.1 to check if it definitely is.

Have you tried checking the site for help.....it's bit hard trying to complain online
11. (Original post by ian.slater)
http://www.wolframalpha.com/input/?i=x^3+-x
Thanks. I think it makes sense.

Because d2y/dx2 is 6x for that, so x is 0 gives a point of inflection but not a stationary point.

That's quite interesting because usually what you get for the 2nd differential is a constant due to terms only being quadratic so it's something new. Thanks.

EDIT: Usually it's not a constant, sorry, but usually when we do find the point of inflection, it's due to finding the gradient to be 0 in the first place, I get it now
12. (Original post by ian.slater)
This is frequently mis-taught at A level. Another wrong idea is that 'if d2y/dx^2 = 0 then you have a point of inflection'. It's true you may have, but on the simple case of y = x^4 the second derivative is zero at the stationary point at the origin. But it's clearly a minimum.
True actually; at A level they stop at d2y/dx^2 - but because I did additional maths FSMQ, I know the use of d3y/dx^3

Ah, I don't believe even in maths there can be so many "lies" that they teach! thought it was only in science when they have to simplify things and so "lie" to us at GCSE.... haha

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