VCE Methods Question Thread!

[jessss0407]

Question 1: (Latex)

School taught me to do things this way but I'll just step you through it!



So you know you're using the product rule (basically u'v + v'u)
Because we have: u, u', v, v', let's get those out of the way first!









And so then we know that:



Then sub it in!





And then we just rearrange it to make it look like the answer you've given!



That's the answer they've stated but you could go more in depth if you wanted to as well (like expanding the last one and factoring a bit)! I think a major problem if differentiation is knowing when to stop simplifying I guess...

Normally when I check my answer for these questions I just use Wolfram Alpha to check (iPad app)

ohh okay thanks so much I think I simplified/factorised which is why I got a different answer.. when would u suggest to stop simplifying/factorising coz I feel as though they take marks off if it's not in simplest form

[jessss0407]

Hey guys!

I have another question..

Let f(x)=x²e^x. Find {x:f'(x)<0}

basically I dont' know how to solve for x for e^xx(x+2)<0


Thanks!

[soNasty]

Use the null factor law I think

[Phenomenol]

Hey guys!

I have another question..

Let f(x)=x²e^x. Find {x:f'(x)<0}

basically I dont' know how to solve for x for e^xx(x+2)<0


Thanks!

e^x is always positive. So you only really need to worry about solving x(x+2)<0. Doing this is easiest graphically.

[IndefatigableLover]

ohh okay thanks so much I think I simplified/factorised which is why I got a different answer.. when would u suggest to stop simplifying/factorising coz I feel as though they take marks off if it's not in simplest form

I don't to be exact... but for me I generally see how much working space and then from that I know how much working I have to do to get my final answer as well as if I can see any factors or any easy expanding/simplifying.
Like the question I answered before was probably a 2/3 mark question imo and if you left it as:



I reckon you'd be given full marks for that if you had some sort of method and stated the rule you used I guess. It's no different if you fully simplified it out though except for the fact if you make a small mistake in your working then you could get it horribly wrong.

(factor out x^2+2x)

(expand the inside)

(take x^2 as a factor)

(take 2/3 as a factor of the inside)

[Orb]

I don't to be exact... but for me I generally see how much working space and then from that I know how much working I have to do to get my final answer as well as if I can see any factors or any easy expanding/simplifying.
Like the question I answered before was probably a 2/3 mark question imo and if you left it as:



I reckon you'd be given full marks for that if you had some sort of method and stated the rule you used I guess. It's no different if you fully simplified it out though except for the fact if you make a small mistake in your working then you could get it horribly wrong.

(factor out x^2+2x)

(expand the inside)

(take x^2 as a factor)

(take 2/3 as a factor of the inside)

Generally when you're solving a chain rule/product rule type of question, you simplify it as much as possible (so that it looks as neat as it possibly can and when any other further factorisation or simplification makes it look more clustered). I think it's usually a 2 mark question, they award 1 mark for the correct application of the rule in question and 1 mark for an appropriate simplification. The last mark should be awarded to you providing it's a reasonable simplified answer to the examiner or marker.

[Orb]

Just a quick question:

When I have a quadratic, let's say 8x^2 + 4x + 2 = 0 and I want to find the discriminant, why do I have to apply b^2 - 4ac from the original equation and why can't I apply it after simplifying it to 4x^2 + 2 + 1 = 0?

[alchemy]

Just a quick question:

When I have a quadratic, let's say 8x^2 + 4x + 2 = 0 and I want to find the discriminant, why do I have to apply b^2 - 4ac from the original equation and why can't I apply it after simplifying it to 4x^2 + 2x + 1 = 0?

It's very important to realise that you can't just simplify like that. Both the equations above are totally different. They have different dilations, different y-axis intercepts, and in some cases dividing the original equation by a common factor will even yield different x-intercepts & number of x-intercepts (giving a completely different discriminant).

[Orb]

It's very important to realise that you can't just simplify like that. Both the equations above are totally different. They have different dilations, different y-axis intercepts, and in some cases dividing the original equation by a common factor will even yield different x-intercepts & number of x-intercepts (giving a completely different discriminant).

Ohh i see.

Yeah, forgot about how they represent quadratics and aren't just simple equations.

Thanks man!

[Rishi97]

f: R⁺ --> R, f(x)= -square root of x
What is the range?
i got - infiniey to 0 inclusive. But the answer says R^-. Why?
Sorry for the horrible maths terms. I don't know how to include square root signs

[Blondie21]

f: R⁺ --> R, f(x)= -square root of x
What is the range?
i got - infiniey to 0 inclusive. But the answer says R^-. Why?
Sorry for the horrible maths terms. I don't know how to include square root signs

Because the domain is R+. This means that 0 is not included! :-)

[Rishi97]

Because the domain is R+. This means that 0 is not included! :-)

ohhhh i get it now. Completely overlooked that information. lol
Thanks Blondie21

[alchemy]

How would I find n in the equation attached?

[IndefatigableLover]

Generally when you're solving a chain rule/product rule type of question, you simplify it as much as possible (so that it looks as neat as it possibly can and when any other further factorisation or simplification makes it look more clustered). I think it's usually a 2 mark question, they award 1 mark for the correct application of the rule in question and 1 mark for an appropriate simplification. The last mark should be awarded to you providing it's a reasonable simplified answer to the examiner or marker.

I definitely agree with everything you've said hamo94! And I do believe that these type of questions are 2 mark questions (except my school puts product/quotient rule as 3 mark questions) especially when going through Checkpoints these type of questions are only worth 2 marks (it's only worth 3 marks if the question asks you to 'evaluate' something or whatever really).

[lArcdeTriomphe]

Just to add on, don't unnecessarily 'simplify' your expressions for derivatives. Keeping that in mind, do make 'obvious simplifications' (this may seem subjective, but it's pretty obvious what you should have to simplify). e.g. VCAA 2013 Exam 1, question 1a: the expression 'x^2*(1/x)' appeared in the answer, by you were expected to simplify that to 'x'.
The general rule is to divide common factors through and to collect like terms. Note that you do NOT need to factorise expressions or 'simplify' them to make them neater unless the question specifically asks for that. I would actually advise against that because you could make algebraic errors in the process and lose the answer mark. In particular, for relatively 'nasty' looking expressions, leaving expressions unfactorised is the better option.
Also avoid having a fraction within a fraction. Some examiners may be picky with it.