Chapter 3.6, Problem 259E

For the following exercises, use the information in the following table to find $h\text{'}\left(a\right)$ at the given value for a.

$x$	$f\left(x\right)$	$f\text{'}\left(x\right)$	$g\left(x\right)$	$g\text{'}\left(x\right)$
0	2	5	0	2
1	1	-2	3	0
2	4	4	1	-1
3	3	-3	2	3

259. [T] The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled by the function $D\left(t\right)=5\sin \left(\frac{\pi }{6}t-\frac{7\pi }{6}\right)+8$ , where t is the number of hours after midnight. Find the rate at which the depth is changing at 6 a.m.