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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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 Summer '11
 Ma'amRosarioExconde
 Critical Point, Derivative, Differential Calculus

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