Chapter 4.2, Problem 63E

To determine

(a)

Show that ( is a critical point if $\cos 4\theta =-\cos 2\theta$.

To determine

(b)

Show that $\cos {\theta }_1=-\cos {\theta }_2$ if and only if ${\theta }_1=\pi \pm {\theta }_2+2\pi k$ for an integer k.

To determine

(c)

Show that $\cos 4\theta =-\cos 2\theta$ if and only if $\theta =\frac{\pi }{2}+2\pi k\text{ or }\theta =\frac{\pi }{6}+\left(\frac{\pi }{3}\right)k$.

To determine

(d)

The critical points and the extreme values.

To determine

(e)

Check the results of critical point against a graph of the function.