(a) dy/dx = 2 sin x cos x - 2 sin x = 2 sin x ( cos x - 1)
when dy/dx = 0,
sin x = 0, or cos x = 1
x = 0, π, 2π
when x = 0, y = 2
when x = π, y = -2
when x = 2π, y = 2
dy/dx = sin 2x - 2 sin x
d²y/dx² = 2 sin 2x cos 2x - 2 cos x
x = 0, d²y/dx² = -2 < 0 ==> maxima
x = π, d²y/dx² = 2 > 0 ==> minima
x = π, d²y/dx² = -2 < 0 ==> maxima
Alternatively, you could use your graphic calculator to solve
for everything
Try yourself for (b) and (c) using the same methods