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Unformatted text preview: Applcation 3 Optimization Problems MAXIMA and MINIMA PROBLEMS OBJECTIV ES : • identify the quantity to be maximized or minimized, • apply the knowledge of derivatives and critical points in solving maximum and minimum problems and • solve maximum and minimum problems with ease and accuracy. A Procedure for Solving Applied Maximum and Minimum Problems (p. 276) Steps in solving maximum and minimum problems . 1.If needed, draw the figure and indicate the unknown parts by variables. 2.Make the necessary representation for the variables used. 3.Determine the quantity, the dependent variable, to be maximized or minimized. 4.Find a formula relating the variables. 5.Express the dependent variable in step 3 in terms of a single variable, the independent variable. 6.Differentiate the dependent variable in terms of the independent variable. 7.Equate the derivative in step 6 to zero, for maximum or minimum value, to find the critical numbers. 8.Answer the problem completely. Example 1 Divide 120 into two parts such that the product of one part and the square of the other is a maximum. Find the numbers. ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 x 3 240x M' x x 2 240x M' 1 x x 2 x 120 M' x x 120 M' : Equation part other the of square the and part one of product the be M part other the be x 120 part one be x Let = = + = = = = = ( 29 = → = = → = ⇒ = = ⇒ = 80 x x 80 x x 3 x 80 3x 3x 240x dx dM 2 ( 29 ( 29 ( 29 ( 29 40 x 120 and 80 x : answer imum...
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This note was uploaded on 10/19/2011 for the course MATH 21 taught by Professor Ma'amrosarioexconde during the Summer '11 term at Mapúa Institute of Technology.
 Summer '11
 Ma'amRosarioExconde
 Critical Point, Derivative, Differential Calculus

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