Let () 2 sin 2 sin 4 (a) Show that is a critical point if cos 4 cos 2 (b) Show, using a unit circle, that cos 1 cos 2 if and only if 1 2 2k for an integer k (c) Show that cos 4 cos 2 if and only if 2 k or 6 ( 3)k (d) Find the six critical points of on 0, 2 and find the extreme values of on this int...

f0 2 sin 20 sin 40 is differentiable at all so the way to find the critical such that ...

Let () = 2 sin 2 + sin 4. (a) Show that is a critical point

Question:

Let ƒ(θ) = 2 sin 2θ + sin 4θ.
(a) Show that θ is a critical point if cos 4θ = − cos 2θ.
(b) Show, using a unit circle, that cos θ₁= − cos θ₂if and only if θ₁= π ± θ₂+ 2πk for an integer k.
(c) Show that cos 4θ= − cos 2θif and only if θ = π/2+ πk or θ = π/6 +(π/3)k.
(d) Find the six critical points of ƒ on [0, 2π] and find the extreme values of ƒ on this interval.
(e) Check your results against a graph of ƒ.