Warm up 9/25 Finalize your letter to the MANufacture. Be ready to shared.

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3.7 Optimization Problems

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Warm up 9/25 Finalize your letter to the MANufacture. Be ready to shared.

HW Quiz You have escape from Isle Royale and make it back to Minnesotan mainland before the wolves eat you alive! Your rowboat is docked at point A. You can row 3 miles per hour, and you can walk at four miles per hour. Where should you land the boat in order to make it to Gran Marais in the least amount of time. How long does it take you to get there?

Agenda : go over hw Review problems Be seated before the bell rings DESK Agenda : go over hw Review problems Warm-up (in your notes) homework

Notebook 17) Optimization HW: pg221. p21,23,25,33,35,41 Learning Target 1 Table of content Page 13) Extreme Values 14) Role’s Thm MVT 15) Increasing/Decreasing & 1st deriv. Test 16) Concavity and 2nd deri. Test 17) Optimization 1 LT3: Solve optimization problems HW: pg221. p21,23,25,33,35,41

2. Maximum Volume problem Determine the dimensions of a rectangular solid ( with a square base) of maximum volume if its surface area is 150 square inches. By 2nd derivative test, x = 5 yield the maximum value

3. Minimum Area problem A rectangular page is to contain 36 square inches of print. The margins on each side are to be 1.5 inches. Find the dimensions of the page such that the least amount of paper is used.

4. A cylindrical can with a closed top and bottom is to be made to have a volume of 1 gallon (about 231 cubic inches). The material used to make the bottom and top cost $0.06 per square inch and the material costs $0.03 per square inch. Find the dimensions of the can to minimize the total cost. What will the total cost be?

5. What are the dimensions and the area of the largest rectangle that can be inscribed in a semicircle of radius 2?

What are the dimensions and the area of the largest rectangle that can be inscribed in a semicircle of radius 2? Maximize Area A = 2xy

Practice with white boards No notes No graphing calculators

Determine if MVT applies. If so find the c, if not explain why.

Find interval where the function is increasing or decreasing