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Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Question
Chapter 4.3, Problem 34PS
To determine
Relative
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6. Use the first derivative to determine where the function is increasing and decreasing and where all relative maximums and minimums occur. Do not use the graph
5.
Fore each of the following find the values of x where f is: 1)increasing; 2)decreasing; 3)has relative maximum, and; 4)has relative minimum points (use the first derivative test) and find these points:
(a). f(x) = 3x2 - 3x2 - 9x
(b). f(x) = sinx on [0. 2pi]
(c). f(x) = (1/5)x5 - (5/3)x3 + 4x +1
(d). f(x) = (x-2)/(x+2)
(e). f(x) = (1 - x)2(1 + x)3
Make a number line to identify intervals by plotting the critical numbers obtained from problem#1 of the function f(t) = 2t3+3t2-12t+7.
Choose a value of x or test point in every interval and substitute it to the first derivative. Identify the increasing and decreasing intervals.
Chapter 4 Solutions
Calculus
Ch. 4.1 - Prob. 1PSCh. 4.1 - Prob. 2PSCh. 4.1 - Prob. 3PSCh. 4.1 - Prob. 4PSCh. 4.1 - Prob. 5PSCh. 4.1 - Prob. 6PSCh. 4.1 - Prob. 7PSCh. 4.1 - Prob. 8PSCh. 4.1 - Prob. 9PSCh. 4.1 - Prob. 10PS
Ch. 4.1 - Prob. 11PSCh. 4.1 - Prob. 12PSCh. 4.1 - Prob. 13PSCh. 4.1 - Prob. 14PSCh. 4.1 - Prob. 15PSCh. 4.1 - Prob. 16PSCh. 4.1 - Prob. 17PSCh. 4.1 - Prob. 18PSCh. 4.1 - Prob. 19PSCh. 4.1 - Prob. 20PSCh. 4.1 - Prob. 21PSCh. 4.1 - Prob. 22PSCh. 4.1 - Prob. 23PSCh. 4.1 - Prob. 24PSCh. 4.1 - Prob. 25PSCh. 4.1 - Prob. 26PSCh. 4.1 - Prob. 27PSCh. 4.1 - Prob. 28PSCh. 4.1 - Prob. 29PSCh. 4.1 - Prob. 30PSCh. 4.1 - Prob. 31PSCh. 4.1 - Prob. 32PSCh. 4.1 - Prob. 33PSCh. 4.1 - Prob. 34PSCh. 4.1 - Prob. 35PSCh. 4.1 - Prob. 36PSCh. 4.1 - Prob. 37PSCh. 4.1 - Prob. 38PSCh. 4.1 - Prob. 39PSCh. 4.1 - Prob. 40PSCh. 4.1 - Prob. 41PSCh. 4.1 - Prob. 42PSCh. 4.1 - Prob. 43PSCh. 4.1 - Prob. 44PSCh. 4.1 - Prob. 45PSCh. 4.1 - Prob. 46PSCh. 4.1 - Prob. 47PSCh. 4.1 - Prob. 48PSCh. 4.1 - Prob. 49PSCh. 4.1 - Prob. 50PSCh. 4.1 - Prob. 51PSCh. 4.1 - Prob. 52PSCh. 4.1 - Prob. 53PSCh. 4.1 - Prob. 54PSCh. 4.1 - Prob. 55PSCh. 4.1 - Prob. 56PSCh. 4.1 - Prob. 57PSCh. 4.1 - Prob. 58PSCh. 4.1 - Prob. 59PSCh. 4.1 - Prob. 60PSCh. 4.2 - Prob. 1PSCh. 4.2 - Prob. 2PSCh. 4.2 - Prob. 3PSCh. 4.2 - Prob. 4PSCh. 4.2 - Prob. 5PSCh. 4.2 - Prob. 6PSCh. 4.2 - Prob. 7PSCh. 4.2 - Prob. 8PSCh. 4.2 - Prob. 9PSCh. 4.2 - Prob. 10PSCh. 4.2 - Prob. 11PSCh. 4.2 - Prob. 12PSCh. 4.2 - Prob. 13PSCh. 4.2 - Prob. 14PSCh. 4.2 - Prob. 15PSCh. 4.2 - Prob. 16PSCh. 4.2 - Prob. 17PSCh. 4.2 - Prob. 18PSCh. 4.2 - Prob. 19PSCh. 4.2 - Prob. 20PSCh. 4.2 - Prob. 21PSCh. 4.2 - Prob. 22PSCh. 4.2 - Prob. 23PSCh. 4.2 - Prob. 24PSCh. 4.2 - Prob. 25PSCh. 4.2 - Prob. 26PSCh. 4.2 - Prob. 27PSCh. 4.2 - Prob. 28PSCh. 4.2 - Prob. 29PSCh. 4.2 - Prob. 30PSCh. 4.2 - Prob. 31PSCh. 4.2 - Prob. 32PSCh. 4.2 - Prob. 33PSCh. 4.2 - Prob. 34PSCh. 4.2 - Prob. 35PSCh. 4.2 - Prob. 36PSCh. 4.2 - Prob. 37PSCh. 4.2 - Prob. 38PSCh. 4.2 - Prob. 39PSCh. 4.2 - Prob. 40PSCh. 4.2 - Prob. 41PSCh. 4.2 - Prob. 42PSCh. 4.2 - Prob. 43PSCh. 4.2 - Prob. 44PSCh. 4.2 - Prob. 45PSCh. 4.2 - Prob. 46PSCh. 4.2 - Prob. 47PSCh. 4.2 - Prob. 48PSCh. 4.2 - Prob. 49PSCh. 4.2 - Prob. 50PSCh. 4.2 - Prob. 51PSCh. 4.2 - Prob. 52PSCh. 4.2 - Prob. 53PSCh. 4.2 - Prob. 54PSCh. 4.2 - Prob. 55PSCh. 4.2 - Prob. 56PSCh. 4.2 - Prob. 57PSCh. 4.2 - Prob. 58PSCh. 4.2 - Prob. 59PSCh. 4.2 - Prob. 60PSCh. 4.3 - Prob. 1PSCh. 4.3 - Prob. 2PSCh. 4.3 - Prob. 3PSCh. 4.3 - Prob. 4PSCh. 4.3 - Prob. 5PSCh. 4.3 - Prob. 6PSCh. 4.3 - Prob. 7PSCh. 4.3 - Prob. 8PSCh. 4.3 - Prob. 9PSCh. 4.3 - Prob. 10PSCh. 4.3 - Prob. 11PSCh. 4.3 - Prob. 12PSCh. 4.3 - Prob. 13PSCh. 4.3 - Prob. 14PSCh. 4.3 - Prob. 15PSCh. 4.3 - Prob. 16PSCh. 4.3 - Prob. 17PSCh. 4.3 - Prob. 18PSCh. 4.3 - Prob. 19PSCh. 4.3 - Prob. 20PSCh. 4.3 - Prob. 21PSCh. 4.3 - Prob. 22PSCh. 4.3 - Prob. 23PSCh. 4.3 - Prob. 24PSCh. 4.3 - Prob. 25PSCh. 4.3 - Prob. 26PSCh. 4.3 - Prob. 27PSCh. 4.3 - Prob. 28PSCh. 4.3 - Prob. 29PSCh. 4.3 - Prob. 30PSCh. 4.3 - Prob. 31PSCh. 4.3 - Prob. 32PSCh. 4.3 - Prob. 33PSCh. 4.3 - Prob. 34PSCh. 4.3 - Prob. 35PSCh. 4.3 - Prob. 36PSCh. 4.3 - Prob. 37PSCh. 4.3 - Prob. 38PSCh. 4.3 - Prob. 39PSCh. 4.3 - Prob. 40PSCh. 4.3 - Prob. 41PSCh. 4.3 - Prob. 42PSCh. 4.3 - Prob. 43PSCh. 4.3 - Prob. 44PSCh. 4.3 - Prob. 45PSCh. 4.3 - Prob. 46PSCh. 4.3 - Prob. 47PSCh. 4.3 - Prob. 48PSCh. 4.3 - Prob. 49PSCh. 4.3 - Prob. 50PSCh. 4.3 - Prob. 51PSCh. 4.3 - Prob. 52PSCh. 4.3 - Prob. 53PSCh. 4.3 - Prob. 54PSCh. 4.3 - Prob. 55PSCh. 4.3 - Prob. 56PSCh. 4.3 - Prob. 57PSCh. 4.3 - Prob. 58PSCh. 4.3 - Prob. 59PSCh. 4.3 - Prob. 60PSCh. 4.4 - Prob. 1PSCh. 4.4 - Prob. 2PSCh. 4.4 - Prob. 3PSCh. 4.4 - Prob. 4PSCh. 4.4 - Prob. 5PSCh. 4.4 - Prob. 6PSCh. 4.4 - Prob. 7PSCh. 4.4 - Prob. 8PSCh. 4.4 - Prob. 9PSCh. 4.4 - Prob. 10PSCh. 4.4 - Prob. 11PSCh. 4.4 - Prob. 12PSCh. 4.4 - Prob. 13PSCh. 4.4 - Prob. 14PSCh. 4.4 - Prob. 15PSCh. 4.4 - Prob. 16PSCh. 4.4 - Prob. 17PSCh. 4.4 - Prob. 18PSCh. 4.4 - Prob. 19PSCh. 4.4 - Prob. 20PSCh. 4.4 - Prob. 21PSCh. 4.4 - Prob. 22PSCh. 4.4 - Prob. 23PSCh. 4.4 - Prob. 24PSCh. 4.4 - Prob. 25PSCh. 4.4 - Prob. 26PSCh. 4.4 - Prob. 27PSCh. 4.4 - Prob. 28PSCh. 4.4 - Prob. 29PSCh. 4.4 - Prob. 30PSCh. 4.4 - Prob. 31PSCh. 4.4 - Prob. 32PSCh. 4.4 - Prob. 33PSCh. 4.4 - Prob. 34PSCh. 4.4 - Prob. 35PSCh. 4.4 - Prob. 36PSCh. 4.4 - Prob. 37PSCh. 4.4 - Prob. 38PSCh. 4.4 - Prob. 39PSCh. 4.4 - Prob. 40PSCh. 4.4 - Prob. 41PSCh. 4.4 - Prob. 42PSCh. 4.4 - Prob. 43PSCh. 4.4 - Prob. 44PSCh. 4.4 - Prob. 45PSCh. 4.4 - Prob. 46PSCh. 4.4 - Prob. 47PSCh. 4.4 - Prob. 48PSCh. 4.4 - Prob. 49PSCh. 4.4 - Prob. 50PSCh. 4.4 - Prob. 51PSCh. 4.4 - Prob. 52PSCh. 4.4 - Prob. 53PSCh. 4.4 - Prob. 54PSCh. 4.4 - Prob. 55PSCh. 4.4 - Prob. 56PSCh. 4.4 - Prob. 57PSCh. 4.4 - Prob. 58PSCh. 4.4 - Prob. 59PSCh. 4.4 - Prob. 60PSCh. 4.5 - Prob. 1PSCh. 4.5 - Prob. 2PSCh. 4.5 - Prob. 3PSCh. 4.5 - Prob. 4PSCh. 4.5 - Prob. 5PSCh. 4.5 - Prob. 6PSCh. 4.5 - Prob. 7PSCh. 4.5 - Prob. 8PSCh. 4.5 - Prob. 9PSCh. 4.5 - Prob. 10PSCh. 4.5 - Prob. 11PSCh. 4.5 - Prob. 12PSCh. 4.5 - Prob. 13PSCh. 4.5 - Prob. 14PSCh. 4.5 - Prob. 15PSCh. 4.5 - Prob. 16PSCh. 4.5 - Prob. 17PSCh. 4.5 - Prob. 18PSCh. 4.5 - Prob. 19PSCh. 4.5 - Prob. 20PSCh. 4.5 - Prob. 21PSCh. 4.5 - Prob. 22PSCh. 4.5 - Prob. 23PSCh. 4.5 - Prob. 24PSCh. 4.5 - Prob. 25PSCh. 4.5 - Prob. 26PSCh. 4.5 - Prob. 27PSCh. 4.5 - Prob. 28PSCh. 4.5 - Prob. 29PSCh. 4.5 - Prob. 30PSCh. 4.5 - Prob. 31PSCh. 4.5 - Prob. 32PSCh. 4.5 - Prob. 33PSCh. 4.5 - Prob. 34PSCh. 4.5 - Prob. 35PSCh. 4.5 - Prob. 36PSCh. 4.5 - Prob. 37PSCh. 4.5 - Prob. 38PSCh. 4.5 - Prob. 39PSCh. 4.5 - Prob. 40PSCh. 4.5 - Prob. 41PSCh. 4.5 - Prob. 42PSCh. 4.5 - Prob. 43PSCh. 4.5 - Prob. 44PSCh. 4.5 - Prob. 45PSCh. 4.5 - Prob. 46PSCh. 4.5 - Prob. 47PSCh. 4.5 - Prob. 48PSCh. 4.5 - Prob. 49PSCh. 4.5 - Prob. 50PSCh. 4.5 - Prob. 51PSCh. 4.5 - Prob. 52PSCh. 4.5 - Prob. 53PSCh. 4.5 - Prob. 54PSCh. 4.5 - Prob. 55PSCh. 4.5 - Prob. 56PSCh. 4.5 - Prob. 57PSCh. 4.5 - Prob. 58PSCh. 4.5 - Prob. 59PSCh. 4.5 - Prob. 60PSCh. 4.6 - Prob. 1PSCh. 4.6 - Prob. 2PSCh. 4.6 - Prob. 3PSCh. 4.6 - Prob. 4PSCh. 4.6 - Prob. 5PSCh. 4.6 - Prob. 6PSCh. 4.6 - Prob. 7PSCh. 4.6 - Prob. 8PSCh. 4.6 - Prob. 9PSCh. 4.6 - Prob. 10PSCh. 4.6 - Prob. 11PSCh. 4.6 - Prob. 12PSCh. 4.6 - Prob. 13PSCh. 4.6 - Prob. 14PSCh. 4.6 - Prob. 15PSCh. 4.6 - Prob. 16PSCh. 4.6 - Prob. 17PSCh. 4.6 - Prob. 18PSCh. 4.6 - Prob. 19PSCh. 4.6 - Prob. 20PSCh. 4.6 - Prob. 21PSCh. 4.6 - Prob. 22PSCh. 4.6 - Prob. 23PSCh. 4.6 - Prob. 24PSCh. 4.6 - Prob. 25PSCh. 4.6 - Prob. 26PSCh. 4.6 - Prob. 27PSCh. 4.6 - Prob. 28PSCh. 4.6 - Prob. 29PSCh. 4.6 - Prob. 30PSCh. 4.6 - Prob. 31PSCh. 4.6 - Prob. 32PSCh. 4.6 - Prob. 33PSCh. 4.6 - Prob. 34PSCh. 4.6 - Prob. 35PSCh. 4.6 - Prob. 36PSCh. 4.6 - Prob. 37PSCh. 4.6 - Prob. 38PSCh. 4.6 - Prob. 39PSCh. 4.6 - Prob. 40PSCh. 4.6 - Prob. 41PSCh. 4.6 - Prob. 42PSCh. 4.6 - Prob. 43PSCh. 4.6 - Prob. 44PSCh. 4.6 - Prob. 45PSCh. 4.6 - Prob. 46PSCh. 4.6 - Prob. 47PSCh. 4.6 - Prob. 48PSCh. 4.6 - Prob. 49PSCh. 4.6 - Prob. 50PSCh. 4.6 - Prob. 51PSCh. 4.6 - Prob. 52PSCh. 4.6 - Prob. 53PSCh. 4.6 - Prob. 54PSCh. 4.6 - Prob. 55PSCh. 4.6 - Prob. 56PSCh. 4.6 - Prob. 57PSCh. 4.6 - Prob. 58PSCh. 4.6 - Prob. 59PSCh. 4.6 - Prob. 60PSCh. 4.7 - Prob. 1PSCh. 4.7 - Prob. 2PSCh. 4.7 - Prob. 3PSCh. 4.7 - Prob. 4PSCh. 4.7 - Prob. 5PSCh. 4.7 - Prob. 6PSCh. 4.7 - Prob. 7PSCh. 4.7 - Prob. 8PSCh. 4.7 - Prob. 9PSCh. 4.7 - Prob. 10PSCh. 4.7 - Prob. 11PSCh. 4.7 - Prob. 12PSCh. 4.7 - Prob. 13PSCh. 4.7 - Prob. 14PSCh. 4.7 - Prob. 15PSCh. 4.7 - Prob. 16PSCh. 4.7 - Prob. 17PSCh. 4.7 - Prob. 18PSCh. 4.7 - Prob. 19PSCh. 4.7 - Prob. 20PSCh. 4.7 - Prob. 21PSCh. 4.7 - Prob. 22PSCh. 4.7 - Prob. 23PSCh. 4.7 - Prob. 24PSCh. 4.7 - Prob. 25PSCh. 4.7 - Prob. 26PSCh. 4.7 - Prob. 27PSCh. 4.7 - Prob. 28PSCh. 4.7 - Prob. 29PSCh. 4.7 - Prob. 30PSCh. 4.7 - Prob. 31PSCh. 4.7 - Prob. 32PSCh. 4.7 - Prob. 33PSCh. 4.7 - Prob. 34PSCh. 4.7 - Prob. 35PSCh. 4.7 - Prob. 36PSCh. 4.7 - Prob. 37PSCh. 4.7 - Prob. 38PSCh. 4.7 - Prob. 39PSCh. 4.7 - Prob. 40PSCh. 4.7 - Prob. 41PSCh. 4.7 - Prob. 42PSCh. 4.7 - Prob. 43PSCh. 4.7 - Prob. 44PSCh. 4.7 - Prob. 45PSCh. 4.7 - Prob. 46PSCh. 4.7 - Prob. 47PSCh. 4.7 - Prob. 48PSCh. 4.7 - Prob. 49PSCh. 4.7 - Prob. 50PSCh. 4.7 - Prob. 51PSCh. 4.7 - Prob. 52PSCh. 4.7 - Prob. 53PSCh. 4.7 - Prob. 54PSCh. 4.7 - Prob. 55PSCh. 4.7 - Prob. 56PSCh. 4.7 - Prob. 57PSCh. 4.7 - Prob. 58PSCh. 4.7 - Prob. 59PSCh. 4.7 - Prob. 60PSCh. 4 - Prob. 1PECh. 4 - Prob. 2PECh. 4 - Prob. 3PECh. 4 - Prob. 4PECh. 4 - Prob. 5PECh. 4 - Prob. 6PECh. 4 - Prob. 7PECh. 4 - Prob. 8PECh. 4 - Prob. 9PECh. 4 - Prob. 10PECh. 4 - Prob. 11PECh. 4 - Prob. 12PECh. 4 - Prob. 13PECh. 4 - Prob. 14PECh. 4 - Prob. 15PECh. 4 - Prob. 16PECh. 4 - Prob. 17PECh. 4 - Prob. 18PECh. 4 - Prob. 19PECh. 4 - Prob. 20PECh. 4 - Prob. 21PECh. 4 - Prob. 22PECh. 4 - Prob. 23PECh. 4 - Prob. 24PECh. 4 - Prob. 25PECh. 4 - Prob. 26PECh. 4 - Prob. 27PECh. 4 - Prob. 28PECh. 4 - Prob. 29PECh. 4 - Prob. 30PECh. 4 - Prob. 1SPCh. 4 - Prob. 2SPCh. 4 - Prob. 3SPCh. 4 - Prob. 4SPCh. 4 - Prob. 5SPCh. 4 - Prob. 6SPCh. 4 - Prob. 7SPCh. 4 - Prob. 8SPCh. 4 - Prob. 9SPCh. 4 - Prob. 10SPCh. 4 - Prob. 11SPCh. 4 - Prob. 12SPCh. 4 - Prob. 13SPCh. 4 - Prob. 14SPCh. 4 - Prob. 15SPCh. 4 - Prob. 16SPCh. 4 - Prob. 17SPCh. 4 - Prob. 18SPCh. 4 - Prob. 19SPCh. 4 - Prob. 20SPCh. 4 - Prob. 21SPCh. 4 - Prob. 22SPCh. 4 - Prob. 23SPCh. 4 - Prob. 24SPCh. 4 - Prob. 25SPCh. 4 - Prob. 26SPCh. 4 - Prob. 27SPCh. 4 - Prob. 28SPCh. 4 - Prob. 29SPCh. 4 - Prob. 30SPCh. 4 - Prob. 31SPCh. 4 - Prob. 32SPCh. 4 - Prob. 33SPCh. 4 - Prob. 34SPCh. 4 - Prob. 35SPCh. 4 - Prob. 36SPCh. 4 - Prob. 37SPCh. 4 - Prob. 38SPCh. 4 - Prob. 39SPCh. 4 - Prob. 40SPCh. 4 - Prob. 41SPCh. 4 - Prob. 42SPCh. 4 - Prob. 43SPCh. 4 - Prob. 44SPCh. 4 - Prob. 45SPCh. 4 - Prob. 46SPCh. 4 - Prob. 47SPCh. 4 - Prob. 48SPCh. 4 - Prob. 49SPCh. 4 - Prob. 50SPCh. 4 - Prob. 51SPCh. 4 - Prob. 52SPCh. 4 - Prob. 53SPCh. 4 - Prob. 54SPCh. 4 - Prob. 55SPCh. 4 - Prob. 56SPCh. 4 - Prob. 57SPCh. 4 - Prob. 58SPCh. 4 - Prob. 59SPCh. 4 - Prob. 60SPCh. 4 - Prob. 61SPCh. 4 - Prob. 62SPCh. 4 - Prob. 63SPCh. 4 - Prob. 64SPCh. 4 - Prob. 65SPCh. 4 - Prob. 66SPCh. 4 - Prob. 67SPCh. 4 - Prob. 68SPCh. 4 - Prob. 69SPCh. 4 - Prob. 70SPCh. 4 - Prob. 71SPCh. 4 - Prob. 72SPCh. 4 - Prob. 73SPCh. 4 - Prob. 74SPCh. 4 - Prob. 75SPCh. 4 - Prob. 76SPCh. 4 - Prob. 77SPCh. 4 - Prob. 78SPCh. 4 - Prob. 79SPCh. 4 - Prob. 80SPCh. 4 - Prob. 81SPCh. 4 - Prob. 82SPCh. 4 - Prob. 83SPCh. 4 - Prob. 84SPCh. 4 - Prob. 85SPCh. 4 - Prob. 86SPCh. 4 - Prob. 87SPCh. 4 - Prob. 88SPCh. 4 - Prob. 89SPCh. 4 - Prob. 90SPCh. 4 - Prob. 91SPCh. 4 - Prob. 92SPCh. 4 - Prob. 93SPCh. 4 - Prob. 94SPCh. 4 - Prob. 95SPCh. 4 - Prob. 96SPCh. 4 - Prob. 97SPCh. 4 - Prob. 98SPCh. 4 - Prob. 99SP
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- - 2. Suppose ƒ'(x) = (x − 1)¹⁰(x + 2)9⁹99 (x+3)(x + 5)³(x − 2)¹2000. Find all values of x for which f(x) attains a local maximum or minimum. Hint: you can reason about where f'(x) is positive or negative without actually computing the full value of f'(x).arrow_forward11) A consumer's level of utility from consuming a certain good s is given by the following function: U(x) = 1.5x² - 12 Due to a shift in the consumer's taste and preferences they will now derive 2 more units of utility for consuming the same amount of good x as before. (a) Sketch the original utility function of good .x. (b) Why is it necessary that x > 0? (c) Determine the new utility function of this company. (d) Using your graph in (i) sketch the transformed utility function. for x > 0arrow_forward10. DERIVATIVES OF Activity 10.7.5 While the quantity of a product demanded by consumers is often a function of the price of the product, the demand for a product may also depend on the price of other products. For instance, the demand for blue jeans at Old Navy may be affected not only by the price of the jeans themselves, but also by the price of khakis. Suppose we have two goods whose respective prices are p₁ and Pp2. The demand for these goods, q1 and 92, depend on the prices as 91150-2p1 - P2 92 = 200-P1-3p2- The seller would like to set the prices p₁ and p2 in order to maximize revenue. We will assume that the seller meets the full demand for each product. Thus, if we let R be the revenue obtained by selling q₁ items of the first good at price pi per item and q2 items of the second good at price p2 per item, we have R= P191 +P292- We can then write the revenue as a function of just the two variables pi and p2 by using Equations (10.7.1) and (10.7.2), giving us R(P1, P2) = P1…arrow_forward
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