You are Here: Home

# C2 Question on Differentiation

Announcements Posted on
Talking about ISA/EMPA specifics is against our guidelines - read more here 28-04-2016
1. Hi All,
I'm studying C2 differentiation and think I've just about cracked it, but I just can't work out the 'maximum' bit at the end.
Basis of question is that Perimeter of shape of rectangle with semicircular top is 40cm, and that area = 40r-2r^2-1/2Pir^2. I've worked it all out and have found that r =40/4+Pi.
When I now put this back into the original formula substituting r for 40/4+Pi, I get A = 40 x 40/4+Pi - 2 x (40/4+Pi)^2 - 1/2 Pi (40/4+Pi)^2. And then I can't get any further. The next bit SHOULD be A = 1600/4+Pi - (2 + 1/2 Pi) (40/4+Pi)^2, but I have no idea how you get there. I'm teaching myself A Level Maths and I think I've missed out on some basic adding and multiplication of fractions and powers. Please can someone show me the steps one by one, and advise me on what I can study further to get to grips with these formulas?
Many thanks
J
2. (Original post by jrowe)
Hi All,
I'm studying C2 differentiation and think I've just about cracked it, but I just can't work out the 'maximum' bit at the end.
Basis of question is that Perimeter of shape of rectangle with semicircular top is 40cm, and that area = 40r-2r^2-1/2Pir^2. I've worked it all out and have found that r =40/4+Pi.
When I now put this back into the original formula substituting r for 40/4+Pi, I get A = 40 x 40/4+Pi - 2 x (40/4+Pi)^2 - 1/2 Pi (40/4+Pi)^2. And then I can't get any further. The next bit SHOULD be A = 1600/4+Pi - (2 + 1/2 Pi) (40/4+Pi)^2, but I have no idea how you get there. I'm teaching myself A Level Maths and I think I've missed out on some basic adding and multiplication of fractions and powers. Please can someone show me the steps one by one, and advise me on what I can study further to get to grips with these formulas?
Many thanks
J
ill give you the general gist, when working a maximum. differentiate the equation and then make it equal to zero. If you have 2 solutioins differentiate the equation again to get the second derivative and plug in the solutions one at a time, if its less than zero it is a maximum. If it is more than zero it is a minimum. Hope that helps.. are you yr 11?
3. (Original post by jrowe)
Hi All,
I'm studying C2 differentiation and think I've just about cracked it, but I just can't work out the 'maximum' bit at the end.
Basis of question is that Perimeter of shape of rectangle with semicircular top is 40cm, and that area = 40r-2r^2-1/2Pir^2. I've worked it all out and have found that r =40/4+Pi.
When I now put this back into the original formula substituting r for 40/4+Pi, I get A = 40 x 40/4+Pi - 2 x (40/4+Pi)^2 - 1/2 Pi (40/4+Pi)^2. And then I can't get any further. The next bit SHOULD be A = 1600/4+Pi - (2 + 1/2 Pi) (40/4+Pi)^2, but I have no idea how you get there. I'm teaching myself A Level Maths and I think I've missed out on some basic adding and multiplication of fractions and powers. Please can someone show me the steps one by one, and advise me on what I can study further to get to grips with these formulas?
Many thanks
J
Start by factoring . Also, you should simplify all the fractions.
4. My knowledge of some of the basics is so bad, especially when it comes to division. So (40/4+Pi) can be changed to (40/4) + Pi and still be the same equation? If so, then ((40/4) + Pi)^2 works out as Pi^2 + 20Pi + 100. Is that right?? What should the next step be?
5. Just looked at my last reply and have worked out that 40/(4+pi) is not the same as (40/4) + pi so please ignore last post! I think I've got some way towards an answer. I realised that the common factor of the equation is (40/(4+pi)) so the equation then becomes 40/(4+pi) [40 - 80/(4+pi) -20pi/(4+pi) ] but how do I then simplify [40 - 80/(4+pi) - 20pi/(4+pi)] ???
6. (Original post by jrowe)
Just looked at my last reply and have worked out that 40/(4+pi) is not the same as (40/4) + pi so please ignore last post! I think I've got some way towards an answer. I realised that the common factor of the equation is (40/(4+pi)) so the equation then becomes 40/(4+pi) [40 - 80/(4+pi) -20pi/(4+pi) ] but how do I then simplify [40 - 80/(4+pi) - 20pi/(4+pi)] ???

7. Ok, this is the bit I don't understand. If you have -2 x (40/(4+pi)^2 - 1/2pi x (40/(4+pi)^2 because there are two brackets the same you can then do ( -2 x - 1/2 pi ) and multiply it by one of the (40/(4+pi)^2. Can someone give me an example of this with much simpler formulas? Why can you get rid of one of the squared brackets? I can see what is happening but I can't understand why. Thank you everyone for your help, I'm starting to get there!
8. (Original post by jrowe)
If you have -2 x (40/(4+pi)^2 - 1/2pi x (40/(4+pi)^2 because there are two brackets the same you can then do ( -2 x - 1/2 pi ) and multiply it by one of the (40/(4+pi)^2.
Yes except for one thing: it would be a + sign where the x sign is. So (- 2 - 1/2 pi) multiplied by (40/(4 + pi))^2.

(Original post by jrowe)
Can someone give me an example of this with much simpler formulas?
It is a simple technique called factorisation. In simple terms:

Where can be anything.

You are basically transforming a sum into a product.

(Original post by jrowe)
Why can you get rid of one of the squared brackets? I can see what is happening but I can't understand why.
You are not exactly getting rid of them, you are simplifying the expression. Here's an example: say I have three apples and three oranges (mathematically: 3 apples + 3 oranges). Factoring would be to say, I have three "apples and oranges" (mathematically: 3 x (apples + oranges)). In the end, it is the same thing. But most often the second expression (the factored one) will be simpler. Clear?

Not to raise an eyebrow but I don't see how you're getting through differentiation without knowing how factorisation works...?
9. Not to raise an eyebrow but I don't see how you're getting through differentiation without knowing how factorisation works...?[/QUOTE]

Hi, thank you for your reply - raising an eyebrow would be the least expression I'd expect!! I do know basically how to factorise but it doesn't come naturally to me and I sometimes find it difficult to spot the factors if that makes sense?! I think I haven't really understood how important it is to factorise and simplify to obtain an answer.
So... A = 1600/(4+Pi) - (2 + 1/2 Pi) (40/(4+Pi)^2.
A = 1600/(4+Pi) - ((4+Pi)/2) (1600/(4+Pi)^2)
A = 1600/(4+Pi) - 800/(4+Pi)
A = 800/(4+Pi) which is the right answer according to my book!!
My problem is that I don't automatically realise that I need to simplify examples such as (2 + 1/2 Pi) into ((4+Pi)/2) but I suppose it's because I need to always try and reduce down to (4+Pi) to match with the other (4+Pi) so that I can break down the equation even further. It's starting to all make sense now - I think I need to just keep on practising and practising!!! Many thanks for your patience.

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
your full birthday is required
1. Oops, you need to agree to our Ts&Cs to register

Updated: July 22, 2012
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### How to predict exam questions

No crystal ball required

Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups
Study resources
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.