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can you find the derivative of:
\[x(t) = 4\sin(3t)\]

Yes that is the ans of a.what about b and c parts?

so we want to find the maximum of:
\[12\cos(3t)\]

So this basically comes down to finding where the cosine function has it's maximums

and then using the value for the maximum of a cosine in the equation

So, what is the maximum of a cosine function?

yes, so the maximum value for the speed must be:

i think 12

yes

At what time does the speed become 12?

don't know.may be 0

Yes, because cos(x) = 1 when x = 0

which first equation?

the equation for position as a function of time

f(t)=4sin(3t)

yes

what i do with this now? please explain

i put t=0 so position is zero?

Yes

ok.Thanks a lot.

You are welcome