someone got this wrong...Help...?

Question

Find the x-coordinate of all points on the curve y = sin 2x - 2 sin x at which the tangent line is horizontal. Consider the domain x = [0,2). (Enter your answer as a decimal.)

x = ____(smallest value)
x = ____
x = ____ (largest value)

Answer 1

y = sin 2x - 2sin x

y' = 2(cos 2x) - 2(cos x)

2 cos 2x - 2 cos x = 0
2 (2cos^2 x - 1) - 2 cos x = 0
4 cos^2 x - 2 - 2 cos x = 0
2cos^2 x - cos x - 1 = 0

Let z = cos x
2z^2 - z - 1 = 0
(2z + 1)(z + 1) = 0
so...
z = -1/2 and 1

so...

cos x = -1/2 and cos x = 1
x = 120 and 240, and x = 0

So.... Take x = 0, 120, and 240, and plug those back into the original equation (y = sin 2x - 2sin x) and figure out which gives you the highest value and the lowest value.

Answer 2

IT's pretty straightforward. Just take the derivative, set it equal to 0, and solve for all the x values that make it 0.

Doug