Optimization Problems Worksheet
This worksheet focuses on solving optimization problems using calculus, including finding maximum and minimum values of functions.
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Optimization Problems
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Read each problem carefully and use calculus to find the optimal solution. Show all your work.
1. A farmer has 400 meters of fencing and wants to enclose a rectangular field bordering a straight river. No fencing is needed along the river. What dimensions will maximize the area of the field?
2. Find two positive numbers whose sum is 60 and whose product is a maximum.
3. A rectangular box with a square base and no top is to be made from 1200 cm² of material. What is the maximum possible volume of the box?
10000 cm³
8000 cm³
4000 cm³
16000 cm³
4. A cylindrical can is to be made to hold 1000 cm³ of oil. Find the dimensions that will minimize the cost of the metal to make the can (assume the can has a top and a bottom).
5. The second derivative test can be used to determine if a critical point is a local maximum or minimum.
True
False