Unless otherwise specified, the domain of a function f is assumed to be the sent of all real numbers x for which f(x) is a real number.

W(t) = { 17/2 - 3/2cos(t/6) for 0 t 6

{ 10 - 1/5(t-6) for 6 < t 10

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 \lim_{t \to 2} (W(t) - t+) / (t-2)