a quick question on application of calculus (1 Viewer)

[misericordia]

heya, any help would be orsum...
k, my question is:
a particle moves along a straight line so that its displacement x meters from a fixed point O is given by x=1+3cos2t, where t is measured in seconds.
find a time when the particle reaches its max. speed. what is the speed?
someone help please...

 

[Mattamz]

x=1+3cos2t
x'= -2.3sin2t = -6sin2t
x'' = -4cos2t = -4x

from: x'= -6sin2t

|sin2t|<=1
therefore max speed when |sin2t|=1;
x' = -6
therefore max speed is 6m/s

 

[misericordia]

ooooooh thankyou!
EDIT: wait... isnt x''=-12cos2t???

 

[Mattamz]

ooooooh thankyou!
EDIT: wait... isnt x''=-12cos2t???

ooops lol sry my bad:

x'' = -4.3cos2t = -12cost2t = -4(x-1)