Let f ( ) = 2 sin 2 + sin 4. (a) Show that is a critical point if cos 4 = cos 2. (b)
Chapter 4, Problem 59(choose chapter or problem)
Let f ( ) = 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 f on [0, 2] and find the extreme values of f on this interval. (e) Check your results against a graph of f .
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