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Applications of Derivatives Assignment Part 1 Max-Min Problems 1. Find the maximum area that can be enclosed with 3600 m of fencing used to create a rectangular region subdivided into 4 equal sub regions as shown in the diagram. 2. “t” hours after a drug is administered to a patient, the concentration k (t ) of the drug in the body is given by: 2t t +4 How long after the drug is administered is the concentration at a maximum? k (t ) = 2 3. A box with a square base and no top is to have a volume of 4 m3. Find the dimensions of the most economical box. 4. Find the largest rectangle that can be inscribed in an ellipse with equation x2 y 2 + =1 9 4 5. Design a 1 litre oil can shaped like a right cylinder, which uses the least amount of material. 6. A drilling rig 12 km offshore is to be connected to a refinery onshore,20 km down the coast from the rig. If the underwater pipe costs are $40,000 per km and land based pipe costs $30,000 per km, find where best to lay the pipe to minimize the cost. Velocity and Acceleration Problems 7. A particle along a straight line path is moving according to the equation. (s is in metres, t is in seconds) s = t 3 − 9t 2 + 15t (a) Give the equations for velocity and acceleration (b) Determine when the particle is at rest. (c) Determine the distance traveled in the first 10 s. Use a diagram to illustrate the trip. 8. A dynamite blast propels a coyote straight up with an initial velocity of 160 m/s. (a) How high will the coyote go? (b) Find its velocity halfway up. (c) Find its acceleration. (d) Find its velocity when it hits the ground.