1. Find the derivative of the function.
B(t) = 6 + 6e-4t
B'(t) =
2. Differentiate the following function.
y = 8x9
3. Find an equation of the tangent line to the curve at the given point. Y = 4x2 - x3, (1, 3)
y = 4x2 -x3, (1,3)
4. Illustrate by graphing the curve and the tangent line on the same screen.
5. A car-detailing service estimates that its daily cost of waxing q cars is
C(q) = 0.09q2 + 39q + 380.
If the service collects $55 for each car waxing, find the number of cars the service should wax daily in order to maximize profit.
6. Write an equation for a cost function where the fixed costs are $1800 and the variable costs are $5 per unit.
7. Rent-A-Reck Incorporated finds that it can rent 60 cars if it charges $40 for a weekend. It estimates that for each $5 price increase it will rent three fewer cars. What price should it charge to maximize its revenue?
How many cars will it rent at this price?
8. An insurance company has custom envelopes printed for correspondence with its clients. It uses 720 boxes of envelopes annually at a steady rate. It costs $285 for delivery and processing (in addition to the printing costs) each time the company places an order, and it costs $2 per box for annual storage. To minimize costs, how many boxes of envelopes should the company order?
How often should they place an order? (Round your answer to one decimal place.)