Did anyone know that cubics don't have to have stationary points?

[pi]

I got the answers right, but I learnt that TODAY during the exam when checking over the 'c' question that came later on.

Amazing.

[BubbleWrapMan]

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.

[TrueTears]

watchu mean cubics dont have stationary points?

[b^3]

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.

[b^3]

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

[Anon123]

really hate how they put this question and q1.a in, i got destroyed...ehhh

[pi]

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*

[Rationalize]

The way I thought to myself was if a quadratic=0 can have no solutions then a cubic can have no S.P's.

[BubbleWrapMan]

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

[TrueTears]

y=x^3

?

[Lasercookie]

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?

[illuminati]

y=x^3

?

Thats got a stationary point at x= 0 dude
something like 4x^3+x^2+3x+1

[pi]

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

[TrueTears]

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

[Panicmode]

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