calc notes lecture 17

# calc notes lecture 17 - We are going to construct a box...

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Lecture Section Objectives Assignment 17 3.4 Optimization Problems 3.4: 1-23 odd, 27, 33 Understanding Goals: 1. Understand how to write a primary and secondary equation. 2. Understand how to use the first- and second-derivative test to solve real-life optimization problems. Primary equation: an equation gives a formula for the quantity to be optimized. Secondary equation: an equation relates the independent variables of the primary equation, which is used to reduce the primary equation to one with a single independent variable. Example 1 : Find two numbers whose difference is 100 and whose product is a minimum. 1

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Example 2 : We need to enclose a field with a fence. We have 500 feet of fencing material and a building is on one side of the field and so won’t need any fencing. Determine the dimensions of the field that will enclose the largest area. 2
Example 3:

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Unformatted text preview: We are going to construct a box whose base length is 3 times the base width. The material used to build the top and bottom cost \$10/ 2 ft and the material used to build the sides cost \$6/ 2 ft . If the box must have a volume of 50 3 ft , determine the dimensions that will minimize the cost to build the box. 3 Example 4: A sheet of cardboard 3 ft. by 4 ft. will be made into a box by cutting equal-sized squares from each corner and folding up the four edges. What will be the dimensions of the box with largest volume? (Duane Kouba, UCDavis, http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/maxmindirectory/MaxMin.html) Let variable x be the length of one edge of the square cut from each corner of the sheet of cardboard. 4 Example 5: Determine the point(s) on 2 1 y x = + that are closest to (0, 2). 5 6...
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calc notes lecture 17 - We are going to construct a box...

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