ATAR Notes: Forum

Archived Discussion => Mathematics => 2011 => End-of-year exams => Exam Discussion => Victoria => Mathematical Methods CAS => Topic started by: pi on November 09, 2011, 08:10:23 pm

Title: Did anyone know that cubics don't have to have stationary points?
Post by: pi on November 09, 2011, 08:10:23 pm
I got the answers right, but I learnt that TODAY during the exam when checking over the 'c' question that came later on.

Amazing.
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: BubbleWrapMan on November 09, 2011, 08:11:37 pm
Yeah I did. But it's not something that's made obvious, at least, it wasn't taught in my class, I noticed it on my own.
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: TrueTears on November 09, 2011, 08:12:02 pm
watchu mean cubics dont have stationary points?
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: b^3 on November 09, 2011, 08:13:14 pm
Yeah I did. But it's not something that's made obvious, at least, it wasn't taught in my class, I noticed it on my own.
Same, yet I got the question wrong. I drew two diagrams on the left side of the page, one with one sationary point, and one with zero. AND I STILL DIDN'T PUT ZERO DOWN! Stupid exam conditions.
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: b^3 on November 09, 2011, 08:13:56 pm
watchu mean cubics dont have stationary points?
Hes saying did we know that it is possible to have a cubic without a stationary point. e.g. -> http://www.wolframalpha.com/input/?i=x%5E3%2Bx%5E2%2Bx%2B1
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: Anon123 on November 09, 2011, 08:15:07 pm
really hate how they put this question and q1.a in, i got destroyed...ehhh
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: pi on November 09, 2011, 08:16:26 pm
Did you guys get taught about them? Or just random investigations?


I swear I never knew cubics could have no stationary points, it's just by luck that I actually fixed up my answers *phew*

Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: Rationalize on November 09, 2011, 08:18:07 pm
The way I thought to myself was if a quadratic=0 can have no solutions then a cubic can have no S.P's.
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: BubbleWrapMan on November 09, 2011, 08:18:29 pm
watchu mean cubics dont have stationary points?
Hes saying did we know that it is possible to have a cubic without a stationary point. e.g. -> http://www.wolframalpha.com/input/?i=x%5E3%2Bx%5E2%2Bx%2B1
Trolled softly
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: TrueTears on November 09, 2011, 08:23:50 pm
y=x^3

?
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: Lasercookie on November 09, 2011, 08:26:50 pm
x^3+x^2+x+1

dy/dx = 3x^2 + 2x + 1 = 0

So there are no real stationary points, but wouldn't there be a stationary point if you were using complex numbers?
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: illuminati on November 09, 2011, 08:27:27 pm
y=x^3

?

Thats got a stationary point at x= 0 dude :P
something like 4x^3+x^2+3x+1
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: pi on November 09, 2011, 08:27:44 pm
So there are no real stationary points, but wouldn't there be a stationary point if you were using complex numbers?

It's methods, everything is real*.


*except my chance of 40+ raw
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: TrueTears on November 09, 2011, 08:31:36 pm
o? thought u meant stationary p.o.i's

anyways, with regards to laseredd, good q, in R^n refer to http://en.wikipedia.org/wiki/Critical_point_%28mathematics%29

in general check out http://en.wikipedia.org/wiki/Critical_point_%28set_theory%29



so basically... solving it over C^n doesn't make "sense", it becomes more abstract than that, hence where set theory (very abstract branch of pure maths) comes into play :)
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: Panicmode on November 09, 2011, 08:33:26 pm
Yeah, our teacher expressly told us,

"You don't need to worry to much about it because in all likelihood it won't ever come up on any methods exam, but it is possible to have non-stationary points of inflection. You don't have to deal with them, just know they exist"

I remembered this in voice over style fashion as I read this question and laughed a little =D
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: BoredSatan on November 09, 2011, 08:44:46 pm
I actually didnt know until i was plugging random values for k into my cas..

and i actually misred that question for m.. im lucky i got it right
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: acinod on November 09, 2011, 08:56:21 pm
Yeah I just learnt that today, with 5 minutes left on the clock.

I was like, hmmm if the discriminant of the derivative was less than zero, what would happen?

*plugged in values into CAS to graph a cubic where discriminant of derivative was less than zero

HOLY FUCK WHAT IS THIS

*found the inverse of that particular cubic and graphed it on the same page as the original cubic

OHHHHHH SHITTTT
Title: Re: Did anyone know that cubics don't have to have stationary points?
Post by: mickeymouse on November 09, 2011, 10:31:14 pm
Yeah I did. But it's not something that's made obvious, at least, it wasn't taught in my class, I noticed it on my own.
Same, yet I got the question wrong. I drew two diagrams on the left side of the page, one with one sationary point, and one with zero. AND I STILL DIDN'T PUT ZERO DOWN! Stupid exam conditions.

omg same, i was like how? no don't trust it put down 1