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Can a cubic graph have turning points at y=-1 and y=1?

As part of my maths work I have been asked 'Can you find a cubic function that has turning points at y = 1 and y = -1?' I am really stuck and starting to think it is impossible.
I can help with that, send me the prompt
Reply 2
Avatar for davros
davros
16
Original post by Moonlit_Centaur
As part of my maths work I have been asked 'Can you find a cubic function that has turning points at y = 1 and y = -1?' I am really stuck and starting to think it is impossible.

How do you normally find turning points of a function?

Can you work backwards and try to construct a function with the required properties?

If not, why not?
Original post by beyonce_myles
I can help with that, send me the prompt

All we were given was 'Can you find a cubic function that has turning points at y = 1 and y = -1 ?'
Reply 4
Avatar for davros
davros
16
Original post by Moonlit_Centaur
All we were given was 'Can you find a cubic function that has turning points at y = 1 and y = -1 ?'

If you had a general cubic function, do you know a way of finding its turning points?
Original post by Moonlit_Centaur
As part of my maths work I have been asked 'Can you find a cubic function that has turning points at y = 1 and y = -1?' I am really stuck and starting to think it is impossible.

Spoiler alert: It is possible!

Just imagine a positive cubic coming up from negative infinity up to y=1, then turns around and goes down to y=-1, and then goes back up into positive infinity
Reply 6
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davros
16
Original post by BuryMathsTutor
"at y = 1 and y = - 1"

oops - that was a bit off! I was having trouble uploading and grabbed the wrong image. Thanks :smile:
Reply 7
Avatar for davros
davros
16
Example (hopefully correct this time!)

cubic graph 2.png
Original post by davros
Example (hopefully correct this time!)

cubic graph 2.png


Thank you, now I just need a function to go with it.
Original post by davros
If you had a general cubic function, do you know a way of finding its turning points?


I do for a quadratic but not a cubic.
Reply 10
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davros
16
Original post by Moonlit_Centaur
I do for a quadratic but not a cubic.

What level are you working at? AS level? A level? The principles are the same although for a quadratic you have a shortcut because you can complete the square.

Hint: if you look at my example graph you can work out some properties of it that might let you cheat a bit :smile:
Original post by davros
What level are you working at? AS level? A level? The principles are the same although for a quadratic you have a shortcut because you can complete the square.

Hint: if you look at my example graph you can work out some properties of it that might let you cheat a bit :smile:


First year of A level and I only know how to find it by completing the square.
Reply 12
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davros
16
Original post by Moonlit_Centaur
First year of A level and I only know how to find it by completing the square.

So you haven't covered any differentiation in your first year of A level?

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