for 2007 Q10b

part (i)

at P,

part (ii)

now we want to minimise the noise level N, so we differentiate (with respect to x)

remember when you are doing this that L

_{1}, L

_{2} and m are all constants, so you treat them just like you would any number like 2, 5 or 6

now we find any stationary points:

let dN/dx = 0

now we take the cube root of both sides:

and now expand the RHS and make x the subject, giving

Don't know if this is enough...

You might need to keep going and show that this is in fact a minimum... ie find the 2nd derivative, sub this answer in and show that it is > 0

Anyone else know?

PS: Many apologies if there are any mistakes in there... this is my 1st time using LaTeX