Help me please???

Question

A curve has the equation y = 2cos x - cos 2x

(i) Given that sin 2x may be expressed as 2sin x cos x, find the x-coordinate of the stationary point of the curve and determine the nature of this stationary point.

Please show your workings clearly and explain..thks

Answer 1

y = 2cos x - cos 2x
=> dy/dx = -2sin x + 2sin 2x
=> dy/dx = -2sin x + 2sin x cos x
stationary point => dy/dx = 0

=> -2sin x + 2sin x cos x = 0
=> 2sin x ( -1 + cos x) = 0
=> 2sin x = 0 OR -1 + cos x= 0
=> sin x = 0 OR cos x= 1
=> x = ?? OR x = ??

Answer 2

y' = -2sinx +2sin 2x
y' =-2sinx +4sinxcosx
y' = -2sin x(1 -2cos x)
Setting -2sin x equal zero we get x = 0 , pi ,2pi
Setting 1-2cos x = 0 we get x = pi/3 and 5pi/3
So stationary points at 0,pi/3, pi,5pi/3, 2pi over interval [0,2pi]

Answer 3

Do your own homework and get a tutor if you need one.