Exercise 10

Let $s(t) = 3\sin(2(t-\frac{\pi}{6})) + 5$. Find the exact absolute maximum and minimum of $s$ on the provided intervals by testing the endpoints and finding and evaluating all relevant critical numbers of $s$.

1. $[\frac{\pi}{6}, \frac{7\pi}{6}]$

2. $[0, \frac{\pi}{2}]$

3. $[0, 2\pi]$

4. $[\frac{\pi}{3}, \frac{5\pi}{6}]$