MATH CONCEPTS CALCULUS
MATH CONCEPTS CALCULUS MATH 131
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This 3 page Class Notes was uploaded by Evert Christiansen on Wednesday October 21, 2015. The Class Notes belongs to MATH 131 at Texas A&M University taught by Angela Allen in Fall. Since its upload, it has received 15 views. For similar materials see /class/226018/math-131-texas-a-m-university in Mathematics (M) at Texas A&M University.
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Date Created: 10/21/15
Math 131 rcopynghtAngela A1181 Fall 2008 46 Supplement Optimization Problems Note Several of these examples come from your textbook Single Variable Calculus Concepts amp Contexts 3rd ed by Stew art Steps in Solving Optimization Problems Understand the problem7What is the unknown What are the given quantities and or conditions Equot Draw a picture 5 Create a model by assigning variables to quantities and express the model as a function f of one variable Also determine the domain of the function 4 Use the methods of sections 42 and 43 to nd the absolute maximum or minimum of f In particular 0 If the domain off is a closed interval then the closed interval method can be used c If there is only one critical number 0 of the continuous function f on the interval then the second derivative test for local extrema can be used since the local maximumminimum will also be the absolute maximumminimum o In some cases it is easier to use a variant of the rst derivative test for local extrema when there is only one critical number 0 of the continuous function f on the interval Iff x gt 0 for all x lt c and f x lt 0 for all x gt c then fc is the absolute maximum off Iff x lt 0 for all x lt c and f x gt 0 for all x gt c then fc is the absolute minimum off Math 131 rcopynghtAngela Allm Fall 2008 Example pg 306 A farmer has 2400 ft of fencing and wants to fence off a rectangular eld that borders a straight river He needs no fence along the river What are the dimensions of the eld that has the largest area Example pg 307 A cylindrical can is to be made to hold 1 L of oil Find the dimensions that will minimize the cost of the metal to manufacture the can Note I L 1000 cm3 Math 131 rcopynghtAngela Allm Fall 2008 Example 16 pg 312 Find the dimensions of the rectangle of largest area that has its base on the xaxis and its other two vertices above the x axis and lying on the parabola y 8 7 2 Example From a 24inch by 6 inch piece of cardboard square corners are cut out so that the sides fold up to form a box Without a top What should the length and width of each square be to maximize the volume of the box
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