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# GCSE further maths question Watch

1. (Original post by B_9710)
An inflection point is where a curve changes from concave to convex or the other way round. There are cases where the second derivative is 0 but this condition is not necessarily met.
oh ok im not sure i know enough about points of inflection then. What cases would the 2nd derivative be 0 in, where the value for x is not at a coordinate for a point of inflection?
2. (Original post by TheRedGoldfish)
Well there kinda isn't any other way to prove points of inflection without finding the stationary points first because by definition a point of inflection is a stationary point with opposite gradients at either side,
No it isn't.
3. (Original post by TheRedGoldfish)
Well there kinda isn't any other way to prove points of inflection without finding the stationary points first because by definition a point of inflection is a stationary point with opposite gradients at either side,
i dont think in this case because you can jump straight to the 2nd derivative
4. (Original post by Uni12345678)
oh ok im not sure i know enough about points of inflection then. What cases would the 2nd derivative be 0 in, where the value for x is not at a coordinate for a point of inflection?
.
5. (Original post by B_9710)
No it isn't.
Yes, it is.

I studied Real Analysis in my 3rd Year at Uni in Spring and this was one area where we had to really thoroughly investigate.
6. (Original post by B_9710)
.
got it thanks ahaha
7. (Original post by L33t)
Where have you taken this question from, a textbook, paper etc?
Teacher.
8. (Original post by Uni12345678)
i dont think in this case because you can jump straight to the 2nd derivative
It's not a full 100% proof. There is no reasoning as to why you use the 2nd derivative regardless of how correct it is. It's like proving that the derivative of e^x is itself - it's correct... but why?
9. (Original post by TheRedGoldfish)
Yes, it is.

I studied Real Analysis in my 3rd Year at Uni in Spring and this was one area where we had to really thoroughly investigate.
An inflection point need not be a stationary point.
10. (Original post by TheRedGoldfish)
It's not a full 100% proof. There is no reasoning as to why you use the 2nd derivative regardless of how correct it is. It's like proving that the derivative of e^x is itself - it's correct... but why?
i get what you mean now. so theres cases where the 2nd derivative doesnt = 0 so we can use it but we'd need to prove that the points either side of the x value have opposite gradients ( plus/minus).
Thanks
11. (Original post by B_9710)
An inflection point need not be a stationary point.
sorry again but example?
12. (Original post by Uni12345678)
sorry again but example?
The example in the OP.
13. (Original post by L33t)
I'd ask/ email your teacher when you get a chance. Sounds overly hard for a GCSE further maths student. I'd suggest asking them if they have given you the correct question or not seems as though a mistake has been made somewhere with the actual question. I mean with the equation BTW not with the wording or content asked.
You don't cubic formula to do this question. You don't need to solve a cubic at all.
14. There's been a lot of nonsense posted in this thread. I recommend people read B_9710's posts only if they're looking to understand this topic.

(Original post by Ano9901whichone)
Find the points of inflection of the curve and prove that they are indeed inflection points.
I tried dy/dx=0 but it didn't work.
Assuming this is AQA Further Maths : This question is beyond your syllabus.

You only need to clasify stationary points, whether they are maximum, minimum or points of inflection. Checking the gradient either side of the point is a good technique for this.
15. (Original post by L33t)
Calm down you seem very angry on this thread xD
I thought the exact opposite. His posts were calm and clear but most importantly, correct
16. (Original post by L33t)
This is why I suggested asking his teacher about whether or not the question was copied down/ reported to their student properly. Instead we just have people arguing about the technicalities of bloody turning points!
17. (Original post by L33t)
This is why I suggested asking his teacher about whether or not the question was copied down/ reported to their student properly. Instead we just have people arguing about the technicalities of bloody turning points!
Yes you're right but I'm sure it would have helped the OP to see what answers we came up with, and as above we can see we were actually right! Also even if the OP doesn't understand everything here I'm sure it would be beneficial. Of course contacting the teacher is a good thing to do as well and you're perfectly right to suggest that, but this question is beneficial to everyone's learning and in the end it's up to the OP how to take things from there. I think it's better to talk about the technicalities of turning points than to not talk about them on a primarily educational forum.
18. (Original post by L33t)
I just meant it wasn't helpful arguing about turning points and points of inflection when the OP just wanted some help. Everyone who has posted on this thread clearly knows what turning points are (inlcuding the OP), it was just unnecessary arguing for something that, at this level, is clearly some sort of mistake. And yes well done on solving the question, but he'd never get one like that in a GCSE further or additional paper would he/ she?
It wasn't supposed to be a particularly hard question I don't think.
19. (Original post by Ano9901whichone)
It wasn't supposed to be a particularly hard question I don't think.
Are you doing AQA GCSE Further Maths?*
20. (Original post by Ano9901whichone)
It wasn't supposed to be a particularly hard question I don't think.
I did AQA GCSE further maths last year. In my opinion this could very well come up since 2nd derivatives are on the syllabus, and i think it wouldnt be the hardest on the paper but it would be harder than most i think

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