Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f ( x ) is a real number.
W ( t ) = { 17/2 − 3/2 cos( π t/6 ) for 0 ≤ t ≤ 6
10− 1/5 ( t − 6 )^2 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 (W(t)−t^3+1/4)/t−2.
t→2
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