VCE Methods Question Thread!

[BubbleWrapMan]

Only functions are really differentiable, so you can only really talk about a circle being differentiable if you express it as two functions. You wouldn't really talk about a circle being differentiable or not, though; certainly you can say that is undefined, and that , which demonstrates that the idea of differentiability doesn't really apply to implicit curves.

[shadows]

If F(x) = f(g(x))


How is
F'(x)=f'(g(x)) x g'(x)

[Phy124]

If F(x) = f(g(x))


How is
F'(x)=f'(g(x)) x g'(x)

We know that the chain rule is:



We can write this as:



Which is equal to 

[shadows]

Thanks...

Another question

Y=x/(1-x)

Show express dy/dx in terms of y


( how does it equal (y+1)^2)

[Markkiieee]

Thanks...

Another question
Y=x/(1-x)
Show express dy/dx in terms of y
( how does it equal (y+1)^2)

It equals 1/(1-x)^2

(Hopefully I haven't made any mistakes)

Use quottient rule: v x u' - u x v'

let v = 1-x
v' = -1
let u = x
u' = 1

plug it into the rule,
1-x times 1 - x times -1/(1-x)^2
= 1 - x + x/(1-x)^2
= 1/(1-x)^2

turns out I'm wrong, ignore this post.

[Conic]

Thanks...

Another question

Y=x/(1-x)

Show express dy/dx in terms of y


( how does it equal (y+1)^2)

Rearrange to get x in terms of y:









Differentiate:







This is more of a spesh approach, but you can do it using substitution too:





Rearrange the original formula to get

Substitute into the derivative:

[Alwin]

Thanks...

Another question

Y=x/(1-x)

Show express dy/dx in terms of y

( how does it equal (y+1)^2)

If you're not comfortable with the spesh method of 'flipping' the derivative or substitution,



I'm assuming you can use the quotient rule to differentiate to get:



All that's required is a bit of algebraic manipulation

since (1-x)^2 same as (x-1)^2

take out the power

plus and minus x

split into two fractions

simplifying, since y=x/(1-x)

Hence, as required

Just another purely methods way of doing it

[shadows]

 1/(dy/dx)=dy/dx,       This looks like a very handy rule to remember.

I don't think this is in the study design for methods.

So VCAA don't mind if we use other techniques? As long as we get the answer?

[shadows]

OH LOL, oh now that makes sense...

[Alwin]

1/(dy/dx)=dy/dx,       This looks like a very handy rule to remember.

I don't think this is in the study design for methods.

So VCAA don't mind if we use other techniques? As long as we get the answer?

Sorry, but that statement is only partially correct. VCAA generally tolerates spesh techniques such as: double diff to find nature of turning points (unless explicitly stated to use a sign table - then ofc use a sign table in this case), methods and rules for differentiation and / or integration if applicable.

HOWEVER. you cannot use technquies outside of the VCE maths course. For example, when I asked about integration by parts (not on spesh or methods course), last year I was told quite firmly that it is not accepted. The answer, if correct, would only get 1 mark. no credit for the working since it is outside of VCE maths.

Someone may, however, correct me on using double diff to find turning points. Teacher opinion varies between schools, but the general consensus is it is allowed - mentioned in a past methods exam 1 I think. The comment said something about how students undertaking Specialist Maths used double diff in the question, but as they did not ask for a sign table it was accepted and awarded marks. I think.

But long story short, always in a methods exam there are methods ways of solving questions, so you shouldnt need spesh rules! also if u don't do spesh they might confuse u no offense

[b^3]

Note: Mod EDIT: Split, and merged topics into spesh thread

[Professor Polonsky]

Sorry, but that statement is only partially correct. VCAA generally tolerates spesh techniques such as: double diff to find nature of turning points (unless explicitly stated to use a sign table - then ofc use a sign table in this case), methods and rules for differentiation and / or integration if applicable.

HOWEVER. you cannot use technquies outside of the VCE maths course. For example, when I asked about integration by parts (not on spesh or methods course), last year I was told quite firmly that it is not accepted. The answer, if correct, would only get 1 mark. no credit for the working since it is outside of VCE maths.

Someone may, however, correct me on using double diff to find turning points. Teacher opinion varies between schools, but the general consensus is it is allowed - mentioned in a past methods exam 1 I think. The comment said something about how students undertaking Specialist Maths used double diff in the question, but as they did not ask for a sign table it was accepted and awarded marks. I think.

But long story short, always in a methods exam there are methods ways of solving questions, so you shouldnt need spesh rules! also if u don't do spesh they might confuse u no offense

I'll double check in regards to methods, because I have been getting mixed responses.

I'm pretty sure that in spesh, there is a very wide latitude for allowed techniques.

[pi]

I don't see why the debate regarding double diff is relevant when no-one seems to be 100% certain of the answer.

If you are a student capable of using double diff, you're not the type of student that wouldn't have the time to spare (extra 1 min?) to draw up a table to prove a stationary point is what it is.

^That's the "safe" route I would take until someone digs up where VCAA said that double diff was a legit technique for methods (some Bulletin)

[shadows]

Regarding finding nature of T.Ps

(say it was a  pos cubic, and there were x value of T.Ps was x=0 and x=2)

could you just say x=0 is a maximum stating that a pos cubic with 2 T.PS, the first T.P will be a maximum? Or would you need to prove it by double derivative/ table method?

[Markkiieee]

Regarding finding nature of T.Ps

(say it was a  pos cubic, and there were x value of T.Ps was x=0 and x=2)

could you just say x=0 is a maximum stating that a pos cubic with 2 T.PS, the first T.P will be a maximum? Or would you need to prove it by double derivative/ table method?

double derivative isn't allowed in methods
if u were looking at the TP where x=0, make x = -1 and x = 1 and solve. that way you can see if the point is a max, min or point of inflection.  and yes the first tp would be a maximum and second a minimum for a normal cubic

edit: after being a member on AN for 3 years, I've finally been able to help someone on the methods thread hope I'm right