c) Find . d) i) Find the value which gives the maximum volume of the box. ii) Calculate the maximum volume of the box. 4. A farmer has a rectangular enclosure with a straight hedge running down one side. The area of the enclosure is 162 m2. He encloses this area using meters of the hedge on one side as shown on the diagram below. a) If he uses meters of fencing to complete the enclosure, show that . The farmer wishes to use the least amount of fencing. b) Find c) Find the value of which makes a minimum d) Calculate this minimum value of . e) find the values of and in the following table. f) Draw an accurate graph of this function using a horizontal scale starting at 0 and taking 2 cm to represent 10 meters, and a vertical scale starting at 30 with 4 cm to represent 10 meters. g) Write down the values of for which increases. IB Math Studies Year 2 6.7 Modeling with Calculus – Mixed IB Paper 2 Problems 5. A shipping container is to be made with six rectangular as shown in the diagram. The dimensions of the container are length height . All of the measurements are in metres. The total length of all twelve edges is 48 metres. a) Show that . [3] b) Show that the volume m3 of the container is given by
c) Find . d) i) Find the value which gives the maximum volume of the box. ii) Calculate the maximum volume of the box. 4. A farmer has a rectangular enclosure with a straight hedge running down one side. The area of the enclosure is 162 m2. He encloses this area using meters of the hedge on one side as shown on the diagram below. a) If he uses meters of fencing to complete the enclosure, show that . The farmer wishes to use the least amount of fencing. b) Find c) Find the value of which makes a minimum d) Calculate this minimum value of . e) find the values of and in the following table. f) Draw an accurate graph of this function using a horizontal scale starting at 0 and taking 2 cm to represent 10 meters, and a vertical scale starting at 30 with 4 cm to represent 10 meters. g) Write down the values of for which increases. IB Math Studies Year 2 6.7 Modeling with Calculus – Mixed IB Paper 2 Problems 5. A shipping container is to be made with six rectangular as shown in the diagram. The dimensions of the container are length height . All of the measurements are in metres. The total length of all twelve edges is 48 metres. a) Show that . [3] b) Show that the volume m3 of the container is given by
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