Assignment1 Name: _ Due Date: _ Max Marks: 96 MCV4U Rubric for marks Knowledge & Identifying the correct derivative rule and applying it to the 2 Understanding problem. Communication Stating the solution in a line statement with correct units. NN Thinking Identify the equation and the constraints Writing all the steps neatly Application Numerically solving the question correctly. Knowledge & Communication Thinking Application Understanding 24 24 24 24 1. Find the dimensions of the rectangle of maximum area with perimeter 1000 feet. 2. You are to make a box with square base and no top. Find the dimensions that minimize the surface area of the box if the volume of the box is to be 32,000 cm3 3. The combined perimeter of a circle and a square is 16. Find the dimensions of the circle and square that produce a minimum total area. 4. Suppose you had to use exactly 200 m of fencing to make either one square enclosure or two separate square enclosures of any size you wished. What plan would give you the least area? What plan would give you the greatest area? 5. An architect is designing a composite window by attaching a semicircular window on top of a rectangular window, so the diameter of the top window is equal to and aligned with the width of the bottom window. If the architect wants the perimeter of the composite window to be 18 ft, what dimensions should the bottom window be in order to create the composite window with the largest area? 6. A geometry student wants to draw a rectangle inscribed in a semicircle of radius 8. If one side must be on the semicircle's diameter, what is the area of the largest rectangle that the student can draw?7. We have a piece of cardboard that is 14 inches by 10 inches and we're going to cut out the corners as shown below and fold up the sides to form a box, also shown below. Determine the height of the box that will give a maximum volume. 14 in 11. A survey indicates that the function S(e) = 340e2 - 4360e + 4500 indicates the relationship between the years of experience, e , that a worker has and annual salary, S, in dollars of employees in a company 10 in = a) Determine the rate of change of salary with respect to education for the value of e i. 10 ii. 12 iii. 16 v. 18 8. A printer needs to make a poster that will have a total area of 200 in' and will have 1-inch b) Refer to your answer in part a). What do you conclude? margins on the sides, a 2-inch margin on the top and a 1.5-inch margin on the bottom as shown c) At what level of education does the rate of change of salary equals $5000 per year of education. below. What dimensions will give the largest printed area? 2 beh margin 12. A store sells 140 stainless steel thermal travel mugs per month at 24 dollars each. A survey indicates that for each $1.50 decrease in price sales will increase by 5 travel mugs. a) Determine the demand function. b) Determine the revenue function c) Determine the marginal revenue d) Solve for R(x)=0. What does it mean? How can the store use this information? 15 inch margin e) What price corresponds to value found in part d) 9. The duck population near a small lake can be modelled by the function d(t) = 0.5(t2 + 8)(t + 4) where t is time in years. a) What is the current duck population? b) Determine the rate of change of duck population in 4 years. c) Determine the rate of change of the duck population when the population is 756 ducks 10. A rock falls from a cliff that is 180 meters high. The distance can be modelled by the functions(t) = 180 - 4.9t2,t 2 0 a) Determine the average velocity of the rock between 1 and 4 seconds b) Determine the velocity of the rock after 4 seconds c) When will the rock hit the ground? d) Determine the impact velocity of the rock Page 2 of 4
