Is the double derivative allowed?

[dehaitest]

Although technically not on the methods course, is the double derivative a suitable method to proving a point is a stationary point?

Could I assume the examiner knows what method I'm using without saying things such as " __ < 0 therefore its a local maximum."

Thanks

[Collin Li]

Short answer: no

Long answer: noooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo (nah, maybe)

It depends on the examiner. The examiner really needs to know of it for him/her to honour it. Also, if you got the question right, then the examiner might not even look twice.

[Mao]

I am not sure what the policy of MM assessment is, but I can tell you that

Could I assume the examiner knows what method I'm using without saying things such as " __ < 0 therefore its a local maximum."

You ALWAYS state what the answer to the question asks. If a question asks you to state the nature of the turning point, and you've drawn out the sign diagram and done all the calculations but did not state it is a maximum/minimum, you will not be awarded full marks.

That goes for questions that says "show that BLAH", your last line should match the question, and put "as required" after it.

[dehaitest]

Thanks for the tips. I'm asking because I've heard from different things from different sources.
(The lecturer today said the double derivative was allowed (TSFX))

[Mao]

I have also heard that UMEP/MUEP techniques are allowed in the specialist exam. But it is always better to not risk it.

[especially when your physics teacher marks physics exams and he doesn't understand mathematics beyond what is required for the physics course, you really stop expecting assessors to know anything beyond the course]

[excal]

Short answer: no

Long answer: noooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo (nah, maybe)

It depends on the examiner. The examiner really needs to know of it for him/her to honour it. Also, if you got the question right, then the examiner might not even look twice.

I lol'd

That ooooo is meant to go for a minute!

[bec]

AN EMAIL I GOT FROM VCAA WHEN I ASKED THEM THE SAME QUESTION:

In general, unless a particular method or approach has been specified, correct and relevant working will be considered by the examiners in assessing student responses to a question, or part of a question.

It is important to note that questions for examination in a given study are devised so that the relevant techniques developed by studying the course content are suitable for answering questions.

While the second derivative can be of assistance in identifying aspects of the behaviour of functions and their graphs, this is not required material for Mathematical Methods(CAS) or Mathematical Methods.

There are some subtleties required for appropriate use of the second derivative, which you can discuss with your teacher.

[shinny]

There are some subtleties required for appropriate use of the second derivative, which you can discuss with your teacher.

I assume this might mean that you have to state WHY its a max/min based on concavity theory...I assume it's like any other thing you use that's outside the course; as long as you prove/explain it, then its fine. For example, we're actually allowed to use differentiation by parts in the spesh exam as long as we derive the formula from the product rule (although I HEAVILY doubt or see any practical application of ever doing this, since all questions that require it will be given as a two-step integration by recognition anyhow)

[Collin Li]

Nah. I don't think the email is saying you have to present the proof. I think it is saying that the method is acceptable, but they would avoid framing their questions where such a method would be far more efficient than using the method taught in Methods 3/4 (i.e: give you a hell of a second derivative).

By "subtleties," I believe they are talking about the conditions for the test to work, and particularly the inconclusive case where the double derivative is equal to zero.

[shinny]

Ah yes, that'd make more sense regarding the 'subtleties'. But still, I don't see why people don't just use sign tables, they're actually EASIER since anything requiring a sign table will be given in the tech exam, and yeh, it's actually alot faster to get the gradient at two points by using your calc than diff'ing by hand and then having to sub in again =\

[Mao]

Ah yes, that'd make more sense regarding the 'subtleties'. But still, I don't see why people don't just use sign tables, they're actually EASIER since anything requiring a sign table will be given in the tech exam, and yeh, it's actually alot faster to get the gradient at two points by using your calc than diff'ing by hand and then having to sub in again =\

not necessarily, using nDerive (on 84), you can plot the second derivative without working out what it is, then just use trace.

if you are using 89, it is even better. give you the second derivative of f(x) at a.

[shinny]

Ah yes, that'd make more sense regarding the 'subtleties'. But still, I don't see why people don't just use sign tables, they're actually EASIER since anything requiring a sign table will be given in the tech exam, and yeh, it's actually alot faster to get the gradient at two points by using your calc than diff'ing by hand and then having to sub in again =\

not necessarily, using nDerive (on 84), you can plot the second derivative without working out what it is, then just use trace.

if you are using 89, it is even better. give you the second derivative of f(x) at a.

Wouldn't you need to show some sort of working out though? Because you wouldn't be able to show much working out if you're getting the numerical value directly from your calc, whereas in a sign table, at least you should've written down the f'(x) somewhere already. Not sure if you'd lose a mark for jumping straight to f"(x)=whatever, therefore whatever without any indication of where you got it from, especially coming from a methods examiner who may not know the technique (although I assume they would if they're teaching maths? o_O). As for the 89, I'm talking about non-CAS students since you'd be able to just get the second derivative in a step =P

[bucket]

at tsfx they said you could use it and included it in their notes

[Mao]

as a general rule, where I used the calculator to work out some answer, I always write down what I've entered in the calculator as a "working out" step.

I'm just saying its doable, and with ease. but I certainly don't recommend anyone to use that.

bucket, whilst they might encourage it, it is not a recommended option. It doesn't save much time at all, and I would believe the paper is written to assess only MM knowledge, not outside of its syllabus