# 6.2 - MATH 1081  Wednesday, March 9   ...

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Unformatted text preview: MATH 1081  Wednesday, March 9    Chapter 6 – Section 2    APPLICATIONS OF EXTREMA    Homework #8 (due 3/14):    Section 6.1 #14, 22, 24, 56                    Section 6.2 #14, 18, 22, 26     Clicker Check­in:  Press any letter to check in now.  Last time, we discussed how to find the absolute extrema of a  function.  In this section, we use these same techniques to solve  problems of optimization, where we are trying to maximize or  minimize some quantity.    As noted in the last section, when finding the absolute extrema  of a function, particular attention must be paid to the domain  of that function.  In the setting of the applications that we will  see today, that continues to be a very important component of  the solution to the problem.    Example:  Section 6.2 #4:  Find nonnegative integers  x  and  y        so that  x + y = 90  and  x 2 y  is maximized.    Example:  Section 6.2 #12:  A fence must be built to enclose a          rectangular area of 20,000 square feet.  Fencing         material costs \$2.50 per foot for the two sides         facing north and south, and \$3.20 per foot for the          other two sides.  Find the cost of the least expensive         fence.    Example:  Section 6.2 #40:  Homing pigeons avoid flying over   large bodies of water….  Assume that a pigeon is  released from a boat 1 mile from the shore of a lake  first flies to a point P on the shore and then along  the straight edge of the shore to its home which is 2  miles from the point on the shore closest to the  boat.  If the pigeon needs 4/3 as much energy to fly  over water as over land, find the location of the  point P which minimizes the energy used.       Example:  Section 6.1 #57:  A piece of wire 12 feet long is cut   into two pieces.  One piece is bent into the shape of  a circle and the other piece is bent into the shape of  a square.  Where should the cut be made to make  the sum of the areas maximum?  Clicker Check­out:  Choose any letter to check out now.      Tomorrow in recitation: Quiz #4 on Sections 4.4, 4.5, 5.1, 5.2, 5.3      There are some potentially useful formulas for geometry in the  appendix of the text (page A‐1).    Next time – Section 6.3      ...
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## This note was uploaded on 05/01/2011 for the course MATH 1081 taught by Professor Johanson during the Spring '08 term at Colorado.

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