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# C2 - Behaviour of polynomials watch

1. Q: For this curve, find where the curve meets the axes, state any symmetry and the behaviour as x -> infinity. Find the coordinates of any stationary points, determine whether they are maximum or minimum points or points of inflexion, and then sketch the curve.

The curve is y=3x^2-x^3

I have done everything above apart from the behaviour part, as I do not understand it. I would really appreciate it if someone explains to me how to do it.
2. (Original post by TarotOfMagic)
Q: For this curve, find where the curve meets the axes, state any symmetry and the behaviour as x -> infinity. Find the coordinates of any stationary points, determine whether they are maximum or minimum points or points of inflexion, and then sketch the curve.

The curve is y=3x^2-x^3

I have done everything above apart from the behaviour part, as I do not understand it. I would really appreciate it if someone explains to me how to do it.
Look at the graph of your function or simply look at the equation, what happens when x gets really really big?
3. (Original post by Zacken)
Look at the graph of your function or simply look at the equation, what happens when x gets really really big?
It gets closer to infinity?....
4. (Original post by TarotOfMagic)
It gets closer to infinity?....
Does it really? Does it get closer to infinity or -infinity?
5. (Original post by Zacken)
Does it really? Does it get closer to infinity or -infinity?
Oh, it gets closer to -infinity, my mistake. But why is this? I think I know why but I can't really put it to words.
6. (Original post by TarotOfMagic)
Oh, it gets closer to -infinity, my mistake. But why is this? I think I know why but I can't really put it to words.
Note that .

Now as , we have that but what happens to the term in the bracket?
7. (Original post by TarotOfMagic)
Oh, it gets closer to -infinity, my mistake. But why is this? I think I know why but I can't really put it to words.
As above, or you could also note that x^3 is miles bigger than x^2, so when you do 3x^2 - x^3 you're doing big number - bigger number which gets you -infinity.
8. (Original post by atsruser)
Note that .

Now as , we have that but what happens to the term in the bracket?
It gets closer to infinity?

Sorry, I have never done this topic.
9. (Original post by TarotOfMagic)
It gets closer to infinity?

Sorry, I have never done this topic.
Nah, you have for really big , you agree with me? So when goes off to infinity, what atsruser has written is , essentially. It's not really a topic, it's more of a logical thing you need to understand and be able to deduce yourself.
10. (Original post by TarotOfMagic)
It gets closer to infinity?

Sorry, I have never done this topic.
No. What does get closer to as ? That's just asking what happens to as we replace with larger and larger numbers (imagine replacing it with 1000, then 1 000 000, then 1 000 000 000 etc.)

How big are the pieces of 3 cakes when you chop them into 1 000 000 pieces?
11. (Original post by Zacken)
So when goes off to infinity, what atsruser has written is , essentially.
Not really. What I've written is and that's true regardless of how big the very big number happens to be.
12. (Original post by atsruser)
Not really. What I've written is and that's true regardless of how big the very big number happens to be.
Sorry, should have phrased it better. I meant "when you plug into what atsruser wrote" instead of saying that that's what you've written.
13. (Original post by Zacken)
Nah, you have for really big , you agree with me? So when goes off to infinity, what atsruser has written is , essentially. It's not really a topic, it's more of a logical thing you need to understand and be able to deduce yourself.
Thanks. I understand it slightly more now. So, the answer is just -infninity?
14. (Original post by TarotOfMagic)
Thanks. I understand it slightly more now. So, the answer is just -infninity?
Kind of, you're meant to say that y diverges off to -infinity, yeah.
15. (Original post by Zacken)
Kind of, you're meant to say that y diverges off to -infinity, yeah.
I checked the answer to this question and it was written minus/plus infinity. Is this the same thing as - infinity?
16. (Original post by TarotOfMagic)
I checked the answer to this question and it was written minus/plus infinity. Is this the same thing as - infinity?
No, it's definitely -infinity. But it means that the examiners are willing to accept any answer that includes infinity, whether it's plus or minus infinity regardless of whether it's correct or not.
17. (Original post by Zacken)
I meant "when you plug into what atsruser wrote"
They're going to beat you with a stick at Cambridge, if you write stuff like that
18. (Original post by atsruser)
They're going to beat you with a stick at Cambridge, if you write stuff like that
I half considered adding a spoiler to disclaim that I know that I'm being completely unrigorous.
19. (Original post by Zacken)
I half considered adding a spoiler to disclaim that I know that I'm being completely unrigorous.
I wonder if they'll accept those in supervision assignments.

"hand waves"

"I know I'm being unrigorous"

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