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 .

Aschool typically sells 500 yearbooks each year for 50 dollars each. the economic calls does a project and discovers that they can sell 100 more yearbooks for every $5 decrease in price. the revenue for yearbook sales is equal to the number of yearbooks sold times the price of the yearbook. let x represent the number of $5 decrease in price. if the expression that represents the revenue is written in the form r(x)=(500+ax)(50-bx). to maximize profit, what price should the school charge for the yearbooks? what is the possible maximum revenue? if the school attains the maximum revenue, how many yearbooks will they sell?

What is the slope simplify your answer and write it as a proper fraction, improper fraction, or integer

Planning for the possibility that your home might get struck by lighting and catch on fire is part of a plan