Math 3A Wksheet #9

Math 3A Wksheet #9 - 1 Jenese Ortiz/Math 3A 3/2-3/3...

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1 Jenese Ortiz/Math 3A 3/2-3/3 08/Week #9/Session 1 Math 3A Worksheet #9 Topics Covered: Optimization (5.4) Examples: 1. Let 𝑌 ( 𝑁 ) be the yield of an agricultural crop as a function of nitrogen level N in the soil. A model that is used for this is 𝑌 𝑁 = 𝑁 1 + 𝑁 2 𝑓𝑜? 𝑁 ≥ 0 (where N is measured in appropriate units). Find the nitrogen level that maximizes yield. 2. A field biologist wants to enclose a rectangular study plot. She has 1600 ft of fencing Using this fencing, what are the dimensions of the study plot that will have the largest area? How to approach Optimization problems: 1. Choose variable: Determine which quantities are relevant, draw a picture, and assign variables. 2. Find the functions and interval: put down all important equations that we need to solve. If the function has 2 variables, use a constraint variable to write f as a function of just 1 variable. 3. Optimize the function: Solve. Find the first derivative and find local min and max.
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2 3. Find the largest possible area of a right triangle where the hypotenuse is 16cm long.
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