URGENT HELP NEEDED BEFORE TOMORROW

[vea]

And in my own opinion, I though that endpoints cannot be increasing or decreasing, therefore it is not included.

I guess I'll have to trust you guys on this one.

[sajib_mostofa]

include include include, i think this question has come up many times and i really can't be bothered writing the definition of strictly increasing/decreasing again, if you don't include you are technically wrong as you are not following set mathematical definitions (conventions).

And if it justs plainly says increasing/decreasing, we don't include?

[lovingit]

My teacher (the chief examiner) says that both include SPs
The difference is if the SP has a horizontal line attached to it on one end, the horizontal line is included in 'non-strictly'
Hope that made some sense

SO does that mean that the VCAA answers for their extended resposne sample q 3b) is wrong
http://www.vcaa.vic.edu.au/vce/studies/mathematics/cas/casexams.html
shouldn't the intervals have sqaure brackets?

[TrueTears]

include it guys, if your teacher says you don't include it then im afriad to say that he/she does not know their definitions. little pendantic definitions like this may seem unimportant to you, but in some areas of mathematics (real analysis), they are very important.

[fady_22]

If the original domain is [0,4], then the increasing domain is ...,4] not round bracket according to my teacher
Increasing is not determined by gradient but whether a point is above or below the next point, so endpoints are included
This is straight from the mouth of the chief examiner this morning

But there would be no point after x=4. So how can the function be increasing here?

[98.40_for_sure]

for simplistic sake, im just gonna include everything that has to do with increasing/decreasing

[TrueTears]

I gave an example here: http://vcenotes.com/forum/index.php/topic,31595.msg326494.html#msg326494

see this question about strictly increasing/decreasing was even on my uni pure maths exam!

[98.40_for_sure]

I gave an example here: http://vcenotes.com/forum/index.php/topic,31595.msg326494.html#msg326494

see this question about strictly increasing/decreasing was even on my uni pure maths exam!

That don't even make sense to me

[the.watchman]

include include include, i think this question has come up many times and i really can't be bothered writing the definition of strictly increasing/decreasing again, if you don't include you are technically wrong as you are not following set mathematical definitions (conventions).

And if it justs plainly says increasing/decreasing, we don't include?

No we do also, please read my earlier post for the difference

[sajib_mostofa]

include include include, i think this question has come up many times and i really can't be bothered writing the definition of strictly increasing/decreasing again, if you don't include you are technically wrong as you are not following set mathematical definitions (conventions).

And if it justs plainly says increasing/decreasing, we don't include?

No we do also, please read my earlier post for the difference

Could you explain what you mean by if the point has a "horizontal line attatched to it at one end"?

[TrueTears]

I gave an example here: http://vcenotes.com/forum/index.php/topic,31595.msg326494.html#msg326494

see this question about strictly increasing/decreasing was even on my uni pure maths exam!

That don't even make sense to me

ok let me try explain it.

a strictly increasing function is a function such that if you pick any value a and b in its domain where a<b then f(b) > f(a)

now say we have a parabola, y = x^2, look at the origin. if we pick a = 0 and b = 1, then clearly f(b) > f(a) so we INCLUDE a = 0

strictly increasing has NOTHING to do with the gradient being 0 or whatever, at x = 0 in y=x^2 we clearly have dy/dx = 0, but we still include the point x =0 since it satisfies the definition of strictly increasing.

mathematics is built on definitions, follow them or you're wrong

get it now? or need further explanations?

[the.watchman]

include include include, i think this question has come up many times and i really can't be bothered writing the definition of strictly increasing/decreasing again, if you don't include you are technically wrong as you are not following set mathematical definitions (conventions).

And if it justs plainly says increasing/decreasing, we don't include?

No we do also, please read my earlier post for the difference

Could you explain what you mean by if the point has a "horizontal line attatched to it at one end"?

Imagine this:

   SP
    |
    v
    ________
   /
 /
|

Say that point was stationary, then you include the whole lot for 'non-strictly' and only the curved bit to the left of the SP for 'strictly'

[becca92]

always always square brackets gotcha

[TrueTears]

And in my own opinion, I though that endpoints cannot be increasing or decreasing, therefore it is not included.

I guess I'll have to trust you guys on this one.

end points are also included, why? read above ^_^

(use y = x^2 as example example again, consider 1<=x=<2, if we pick a = 1.5 and b = 2, f(b)>f(a), does it satisfy the definition? yes. so include)

[vea]

Thanks TT you're my hero.