1) for time 0
a) at time t=3, there are 2.5 cubic feet of water in the tub. write an equation for the locally linear approximation of w at t=3, and use it to approximate the volume of water in the tub at the time.

b)find w"(8). using correct units interpret the meaning of w"(8) in the context of the problem.

c)is there a time t, for 5
d) the tub is in the shape of a rectangular box that is0.5 foot wide, 4 feet long, and 3 feet deep. what is the rate of change of the depth of the water in the tub at time t=6

2)

{17/2 - 3/2cos(pi t/6) for 0< =t< =6
{10 - 1/5(t-6)^2 for 6
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 of 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 limit as t approaches 2 for

lim t -> 2 ( w(t) - t^2 + 3/4) / t - 2