point of inflexion (1 Viewer)

[Arithela]

thanks

 

[Graceofgod]

I have a funny feeling you are asking the wrong question though. Are you sure it asked for the area of the major segment? Because if you have a sector OAB, and a chord AB forming a minor segment, then you are talking about something else...

 

[tommykins]

回复: Re: point of inflexion

To find a horizontal point of inflexion, you solve for f''(x) = 0 and the root must also be a solution to f'(x) = 0.

No

 

[Arithela]

I have a funny feeling you are asking the wrong question though. Are you sure it asked for the area of the major segment? Because if you have a sector OAB, and a chord AB forming a minor segment, then you are talking about something else...

yeah you're right, i skimmed through the 2007 paper and thought i saw 'major segment' when it is indeed 'major sector'

 

[Graceofgod]

=D I am so smart.

But yeah, I have been doing a LOT of maths practice papers recently, and I thought your question was a bit odd

Glad I could help. Good luck

 

[m00]

f''(x) = 0 , remember to show a change in concavity as some schools deduct marks for not showing it

is this also the case for the hsc exam?

 

[Graceofgod]

I would assume so...
If the question asks to find the point(s) of inflexion, then later asks to draw the graph...
Pretty obviously you label the point of inflexion.

However, if it doesn't ask to find any points of inflexion, you can probably get away without marking an exact point.
You can just find from where maximum and minimum turning points are located an approximate location for any points of inflexion.

Don't know if I answered your question, hope that helps

 

[m00]

by showing a change of concavity I mean for example:

if they ask us to find a point of inflexion and it turns out to be (4,2) for example then to check for concavity you gotta prove that f'(3) and f'(5) are both negative or both positive (this proves that it is an inflexion point)

im just wondering if we have to do this in the HSC exam or is finding f''(4) = 0 enough?

 

[Graceofgod]

Oh right I misunderstood the question.

Well I have never heard of that being necessary.

So for that reason I am not qualified to answer, purely because I've never heard or thought about it.

But I do highly doubt it. Official solutions to all the papers I have done never do this.
Also, I have never done it and never been marked down for it.
The only time I can think of it as possibly being necessary is in a question where it hasn't previously been asked in the question to find standing points.
This is because it is technically possible to have the concavity go from for example max, to 0 then back to max again.

EDIT: But I have NEVER seen a graph like this before in a 2u maths paper. It's a bit pedantic..

 

[Timothy.Siu]

by showing a change of concavity I mean for example:

if they ask us to find a point of inflexion and it turns out to be (4,2) for example then to check for concavity you gotta prove that f'(3) and f'(5) are both negative or both positive (this proves that it is an inflexion point)

im just wondering if we have to do this in the HSC exam or is finding f''(4) = 0 enough?

yes u'll have to do that...obviously

if they ask u to find a point of inflexion and say for that example u find (4,2) but if it doesn't change concavity then its not...so u wud be wrong.

 

[Graceofgod]

Ok, I have a devious solution:
Would you be able to get away with
Testing:
When x = 3 When x = 5
f"(x) = positive f"(x) = negative
Therefore (4,2) is point of inflexion.

 

[tommykins]

回复: Re: point of inflexion

No? Because it could be 4.5, 4.6, 4.7 etc. etc.

Lol, prepared for 2unit my ass ;P

 

[Graceofgod]

Haha, as if they would be THAT pedantic... =S
Anyway, if there were standing points or other points of inflexion then you would differ the points obviously.
Otherwise it wouldn't be a problem.

 

[m00]

but the thing is if its f''(x) = 0 its an inflexion point, its like a rule.. there is never an occasion were it isnt, to my understanding i would understand if the question asked to prove it, but is it really necessary to do it when they don't ask specifically?

when asking to prove its a point of inflexion it isnt asking for horizontal or vertical point of inflexion.. just a point of inflexion so f''(x) = 0 should be sufficient ??

 

[tommykins]

回复: Re: point of inflexion

Haha, as if they would be THAT pedantic... =S
Anyway, if there were standing points or other points of inflexion then you would differ the points obviously.
Otherwise it wouldn't be a problem.

are you bloody serious?

 

[Timothy.Siu]

but the thing is if its f''(x) = 0 its an inflexion point, its like a rule.. there is never an occasion were it isnt, to my understanding i would understand if the question asked to prove it, but is it really necessary to do it when they don't ask specifically?

when asking to prove its a point of inflexion it isnt asking for horizontal or vertical point of inflexion.. just a point of inflexion so f''(x) = 0 should be sufficient ??

no. u dont know its a point of inflexion just coz f''(x)=0

u mustn't have been taught properly...

 

[tommykins]

回复: Re: point of inflexion

no. u dont know its a point of inflexion just coz f''(x)=0

u mustn't have been taught properly...

Errr...it's a point of inflexion if f''(x) = 0..

 

[joshlols]

If concavity changes + double derivative = 0 then it's inflexion. Quoted straight from textbook.

 

[Timothy.Siu]

Re: 回复: Re: point of inflexion

Errr...it's a point of inflexion if f''(x) = 0..

nah its not e.g. y=x^4 doesn't have one

 

[tommykins]

回复: Re: 回复: Re: point of inflexion

nah its not e.g. y=x^4 doesn't have one

ah shit yeah, my bad