Stories about Maxima and MinimaSkip to search form Skip to main content. Apparently, many textbooks authors have inferred from this that maximization and minimization cannot be treated at all at the precalculus level. Very few precalculus textbooks present such problems, even in an unsystematic manner. This is a pity; the pursuit ofthis goal should start well befare any calculus course. View PDF. Save to Library.
Absolute & Local Minimum and Maximum Values - Relative Extrema, Critical Numbers / Points Calculus
Maximum and Minimum Word Problems
Exercise 1 If the monetary value of a ruby is proportional to the square of its weight, split a ruby of 2 grams in two parts so that the sum of the values of the two rubies formed is the minimal possible amount. Find, among all the possible straight lines through the point 1, 2 , a line that forms a triangle of minimum area with the positive parts of the cartesian axes. Exercise 3 A buoy formed by two cones of sheet iron joined by its bases has to be constructed by two circular plates with a radius of 3 m. Calculate the dimensions of the buoy so that its volume is maximized. Determine the dimensions of the entire sheet of paper that minimize its surface area. Exercise 5 The monthly net profit, in million of dollars, of a company that manufactures buses is given by the function:. Determine the amount of buses needed to be manufactured each month in order to maximize profits.
Libraries and resellers, please contact cust-serv ams. See our librarian page for additional eBook ordering options. Throughout the history of mathematics, maximum and minimum problems have played an important role in the evolution of the field. Many beautiful and important problems have appeared in a variety of branches of mathematics and physics, as well as in other fields of sciences. The greatest scientists of the past—Euclid, Archimedes, Heron, the Bernoullis, Newton, and many others—took part in seeking solutions to these concrete problems. The solutions stimulated the development of the theory, and, as a result, techniques were elaborated that made possible the solution of a tremendous variety of problems by a single method.
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