C2 Differentiation.

Original post by mynameisntbobk

I've clearly missed something important, can anyone help me see where I went wrong?

For part a) you're interested in the length of the wire. Total length is given as 2.

Reply 2

Original post by ghostwalker

For part a) you're interested in the length of the wire. Total length is given as 2.

Oh yeah. I just realised that. I used (1/2)(pi)(x) as the length of the curve, and it worked

Thank you.

Reply 3

Original post by ghostwalker

For part a) you're interested in the length of the wire. Total length is given as 2.

Do you think you could help me with part c. I was thinking about differentiating the expanded equation, but the pi is off putting, so I'm not sure what I'd do.

Reply 4

Original post by mynameisntbobk

Do you think you could help me with part c. I was thinking about differentiating the expanded equation, but the pi is off putting, so I'm not sure what I'd do.

Yes, I'd do it that way. Expand the brackets and differentiate.

Don't forget pi is just a constant, and as far as calculus is concerned it's no different to any other non-zero constant like, 2, or 7, etc.

See what you can do.

Reply 5

Original post by ghostwalker

I got for my value of x after equalling my dR/dx to be ((4/pi) + 1)

And my max volume to be ((160/pi^2) + 4 + (4/pi))

I know my final answer is wrong though

Reply 6

Original post by mynameisntbobk

I got for my value of x after equalling my dR/dx to be ((4/pi) + 1)

And my max volume to be ((160/pi^2) + 4 + (4/pi))

I know my final answer is wrong though

Your value for x is also incorrect.

I suspect you differentiated correctly, but made a slip when you rearranged it.

Post working for that part, as we can check what's going on.

Reply 7

Original post by ghostwalker

Your value for x is also incorrect.

I suspect you differentiated correctly, but made a slip when you rearranged it.

Post working for that part, as we can check what's going on.

The sheet I worked on is quite messy, so I'll just type it for you.

R = ((-pi * x^2) / 8 ) + x (-x^2/2)

dR/dx = ((-pi * x)/4) + 1 - x

((-pi * x) / 4) + x (-x^2/2) = 0

(-pi * x) + 4 - 4x = 0

(-pi * x) - 4x = -4

x(-pi -4) = -4

x = -4/(-pi -4)

x = (4/pi) + 1

Reply 8

Original post by mynameisntbobk

x = -4/(-pi -4)

x = (4/pi) + 1

Yep. It's the very last line.

You can't simplify the denominator.

You seem to have done a/(b+c)= a/b +a/c which is a definite no, no.

x= 4/(4+pi) is really all you can do.

Reply 9

Original post by ghostwalker

Yep. It's the very last line.

You can't simplify the denominator.

You seem to have done a/(b+c)= a/b +a/c which is a definite no, no.

x= 4/(4+pi) is really all you can do.

Oh right. Thank you so much :smile:

I didn't actually realise I made that mistake, so if I were to put that value of x into the equation for R, that would be fine right?

And sorry to be a burden, but I don't understand part a of question 6

Reply 10

Original post by mynameisntbobk

Oh right. Thank you so much :smile:

I didn't actually realise I made that mistake, so if I were to put that value of x into the equation for R, that would be fine right?

Yep.

And sorry to be a burden, but I don't understand part a of question 6

AP^2 is the distance between A and P squared. So, you'd use Pythagoras on the two sets of co-ordinates.

AP^2 = (difference in x coordinates)^2 +....

Reply 11

Wait a sec i might be acting stupid
but
R = ((-pi * x^2) / 8 ) + x (-x^2/2)

dR/dx = ((-pi * x)/4) + 1 - x

Surely unless its x + (-x^2/2)
it should not be 1- x
rather-x^3/2 --> 3/2 x^2

Reply 12

Original post by ghostwalker

Yep.

AP^2 is the distance between A and P squared. So, you'd use Pythagoras on the two sets of co-ordinates.

AP^2 = (difference in x coordinates)^2 +....

Would I do (8-t)^2 + (-6-t)^2 + (5-2t)^2 ?

I'm sorry, I think the use of 3 points has confused me, I'm usually good with these kinds of questions

Reply 13

So makin

dR/dx = ((-pi * x)/4 -3/2x^2

Reply 14

Any one axplain what i dont get or was it just a typo

Reply 15

science-oliver

Sorry didnt realise part a had been answered :colondollar:

(edited 11 years ago)

Reply 16

Original post by Anony1234

Wait a sec i might be acting stupid
but
R = ((-pi * x^2) / 8 ) + x (-x^2/2)

dR/dx = ((-pi * x)/4) + 1 - x

Surely unless its x + (-x^2/2)
it should not be 1- x
rather-x^3/2 --> 3/2 x^2

Sorry, yeah, I posted that quite ambiguously, it is like you said x + (-x^2/2) or x - (x^2/2)

Sorry about that.

Original post by science-oliver

Sorry didnt realise part a had been answered :colondollar:

Its fine

thanks though.

Reply 17

Original post by mynameisntbobk

Sorry, yeah, I posted that quite ambiguously, it is like you said x + (-x^2/2) or x - (x^2/2)

Sorry about that.

Its fine :smile:

thanks though.

Thats fine :smile:

Thnx for replying thought id gone mad!!

Reply 18

How you doing on 6 If. You need help just use pythagors
ab2 = (8-t) sq +( -6-t )sq+5-2t)sq
= 64 -16t +tsq + 36 +12 t tsq + 4tsq -20t +25
6t^2 -24t+125 there
sorry for presentation sq = squared

Reply 19