The depth of a river at a certain point is modeled by the function W(t) = { 17/2 - 3/2 cos( (t x pi)/6) for 0< or equal to t < or equal to 6; 10 - 1/5 (t - 6)^2 for 6< t < or equal to 10, 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< or equal to t < or equal to 3.5. Use the line tangent to graph of W at t = 3 to show W(3.5). < or equal to 9
C) find lim as x approaches 2 for (W(t) - t^3 + 1/4)/(t - 2)