Calculus Optimization Worksheet
Grade 11 Calculus worksheet focusing on optimization problems involving derivatives and real-world applications.
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Calculus Optimization Worksheet
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Read each problem carefully and show all your work. Use derivatives to find the maximum or minimum values as required. Round answers to two decimal places where appropriate.
1. A farmer has 1200 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area?
2. A cylindrical can is to be made to hold 1000 cm³ of oil. Find the dimensions (radius and height) that will minimize the cost of the metal to make the can. (Assume the top and bottom are made of metal, and ignore thickness).
3. Find the point on the graph of y = x² that is closest to the point (0, 2).
The point on the graph of y = x² closest to (0, 2) is .
4. The sum of two non-negative numbers is 20. What is the maximum product of these two numbers?
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5. A box with a square base and open top must have a volume of 32,000 cm³. Find the dimensions of the box that minimize the amount of material used.