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 = 40r2r^21/2Pir^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
C2 Question on Differentiation
Announcements  Posted on 



(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 = 40r2r^21/2Pir^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 
(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 = 40r2r^21/2Pir^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 
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?

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)] ???

(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)] ???

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!

(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.
(Original post by jrowe)
Can someone give me an example of this with much simpler formulas?
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.
Not to raise an eyebrow but I don't see how you're getting through differentiation without knowing how factorisation works...? 
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.
Reply
Register
Thanks for posting! You just need to create an account in order to submit the post Already a member? Sign in
Oops, something wasn't right
please check the following: