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
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(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.
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