W(t)={17/2−3/2cos(πt6)10−1/5(t−6)2f or0≤t≤6for6
The depth of a river at a certain point is modeled by the function W defined above, where W(t) is measured in feet and time t is measured in hours.

(a) Find W′(8) . Using correct units, explain the meaning of W′(8) in the context of the problem.
(b) The graph of W is concave down for 3≤t≤3.5. Use the line tangent to the graph of W at t=3 to show that W(3.5)≤9.
(c) Find limt→2W(t)−t3+14t−2 .