funky question (2 Viewers)

[kwabon]

just wondering how would you prove this ALGEBRAICALLY, i could do it graphically not algebraically. :-S, prove; sin x - x + (1/6)x^3 >= 0 for x > 0

 

[darusan92]

just wondering how would you prove this ALGEBRAICALLY, i could do it graphically not algebraically. :-S, prove; sin x - x + (1/6)x^3 >= 0 for x > 0

umm.... try differentiating it n prove that it has a positive gradient for x>0 i think they both are the same algebracally and graphically (proving positive gradient)??? just check it in case.....

 

[The Nomad]

Check the inequalities exercise in Cambridge, harder 3U chapter. The last few questions are similar to this if I remember correctly. If not, I'm sure one of the examples is similar to this question.

 

[Trebla]

 

[Trebla]

Edited.

 

[lolokay]

just wondering how would you prove this ALGEBRAICALLY, i could do it graphically not algebraically. :-S, prove; sin x - x + (1/6)x^3 >= 0 for x > 0

differentiate the function, f(x) = sin x - x + (1/6)x^3
f'(x) = cosx - 1 + x^2/2
this is equal to zero when cosx = 0, so this is the minimum or maximum value f(x) in this range
and f''(x) = -sinx + x > 0 for x >0
so this is the minimum value
.'. f(x) > f(0) for x > 0
sin x - x + (1/6)x^3 > 0

 

[kwabon]

kk thanks guys for clearing it up for me.

 

[youngminii]

Lol 1994 HSC question 7

 

[Trebla]

2007 Q7a)

 

[kwabon]

2007 Q7a)

hmmm? what about it?

 

[Aerath]

hmmm? what about it?

I think Trebla means that's where the question is from.

 

[kwabon]

I think Trebla means that's where the question is from.

oh, its actually from 1994, youngminii was right.

 

[Aerath]

oh, its actually from 1994, youngminii was right.

Hmmm, I remember that it was also in 07 as well. Hmm, could be wrong, though.

 

[Trebla]

2007 Q7 a)

http://www.boardofstudies.nsw.edu.au/hsc_exams/exam-papers-2007/pdf_doc/maths-ex2-07.pdf

 

[kwabon]

haha never have done the 07 paper. but yeh was in 1994 as well.

 

[youngminii]

I didn't know they re-used questions word for word..

 

[gurmies]

I differentiated 3 times for this...