Bit stuck :)

f(x)=x|sin(8x)|                              |sin(8x)| = the modulus of sin(8x)

find df/dx , and find values of x where df/dx is not defined.

How far have you made it? Have you actually solved for your df/dx?

Factor theorem? Input values -4 to 4 (excluding zero) into the function. If the answer comnes up with a zero, then you have one of the possible answers.

Then divide the function by the factor, getting the rest of the factors should be easy from then on in.

Chances are one of the factors are between -4 and 4, so this sounds like a good place to start.

Unfortunately exluding zero from your calculation is basically giving him the answer.  Since the differentiation of a |f(x)| function has no value when x=0 you have given him the answer to the second part of the question :)

Who cares about advanced mathematics when he should focus on grammar. :P

@rendo, I don't think this falls anywhere near advanced mathematics, IMO. Grammar is also overrated, ever since the internet was invented proper grammar has become archaic.

I don't know when your coming back Tombi so I'll list the answer.

df/dx = cos(8x)/|cos(8x)|
df/dx is not defined for values of x = n*pi/(n+1) where n is a real odd whole number

Don't know if this is right but I think it is, please correct if I'm wrong

The derivative of x|sin(8x)| is sin(8x) + 8xcos(8x) for values higher than 0 and sin(-8x) - 8xcos(-8x) for values lower than 0. At zero is zero.

It's been a long time since I did actual math work, but I don't think your answer comes up with the correct values where df/dx isn't defined.  You definately need to come out with a df/dx that divides by a sinusodial function becuase the formula will result in a repeating undefined df/dx that occurs 16 times between 0 and 2pi.

So your derivative is definately wrong because there are no undefined df/dx values in your answer.

EDIT: Although I do realise that the 8x does have to come out of the equation, I missed it in my original numbers.  I'm looking to correct my first answer because it is wrong, just wait for me to remember how to do math again.

Okay, so now that I've refreshed my calc days.

df/dx = sin(8x) + 8x*cos(8x)/|cos(8x)| where cos(8x) != 0