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| 1 : | jj | 62 | ## DESCRIPTION |
| 2 : | ## Calculus | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ## KEYWORDS('calculus', 'derivatives') | ||
| 6 : | ## Tagged by YL | ||
| 7 : | |||
| 8 : | ## DBsubject('Calculus') | ||
| 9 : | ## DBchapter('Applications of Differentiation') | ||
| 10 : | ## DBsection('How Derivatives Affect the Shape of a Graph') | ||
| 11 : | ## Date('') | ||
| 12 : | ## Author('') | ||
| 13 : | ## Institution('ASU') | ||
| 14 : | jjholt | 473 | ## TitleText1('Calculus: Early Transcendentals') |
| 15 : | ## EditionText1('5') | ||
| 16 : | jj | 62 | ## AuthorText1('Stewart') |
| 17 : | jjholt | 473 | ## Section1('4.3') |
| 18 : | jj | 62 | ## Problem1('') |
| 19 : | |||
| 20 : | jjholt | 481 | ## TitleText2('Calculus: Early Transcendentals') |
| 21 : | ## EditionText2('6') | ||
| 22 : | ## AuthorText2('Stewart') | ||
| 23 : | ## Section2('4.3') | ||
| 24 : | ## Problem2('') | ||
| 25 : | sh002i | 556 | ## TitleText3('Calculus: Early Transcendentals') |
| 26 : | ## EditionText3('1') | ||
| 27 : | ## AuthorText3('Rogawski') | ||
| 28 : | ## Section3('4.5') | ||
| 29 : | ## Problem3('15') | ||
| 30 : | jjholt | 481 | |
| 31 : | jj | 62 | DOCUMENT(); # This should be the first executable line in the problem. |
| 32 : | |||
| 33 : | loadMacros("PG.pl", | ||
| 34 : | "PGbasicmacros.pl", | ||
| 35 : | "PGchoicemacros.pl", | ||
| 36 : | "PGanswermacros.pl", | ||
| 37 : | "PGauxiliaryFunctions.pl", | ||
| 38 : | "extraAnswerEvaluators.pl"); | ||
| 39 : | |||
| 40 : | |||
| 41 : | $a = random(2,9,1); | ||
| 42 : | $b = non_zero_random(-3,3,1); | ||
| 43 : | |||
| 44 : | TEXT(beginproblem()); | ||
| 45 : | |||
| 46 : | $showPartialCorrectAnswers = 1; | ||
| 47 : | |||
| 48 : | TEXT(EV2(<<EOT)); | ||
| 49 : | Suppose that | ||
| 50 : | \[ f(x) = $a x^2 - x^3 ? {$b}. \] | ||
| 51 : | $BR | ||
| 52 : | |||
| 53 : | (A) Find all critical numbers of \(f\). | ||
| 54 : | If there are no critical numbers, enter 'NONE'. | ||
| 55 : | $BR | ||
| 56 : | Critical numbers = \{ans_rule(25)\} | ||
| 57 : | $PAR | ||
| 58 : | EOT | ||
| 59 : | |||
| 60 : | gage | 268 | ANS(number_list_cmp( "0,2*$a/3" , strings=>["none"] )); |
| 61 : | jj | 62 | |
| 62 : | TEXT(EV2(<<EOT)); | ||
| 63 : | (B) Use interval notation to indicate where \( f(x) \) is increasing. | ||
| 64 : | $BR | ||
| 65 : | $BBOLD Note: $EBOLD Use 'INF' for \(\infty\), '-INF' for \(-\infty\), | ||
| 66 : | and use 'U' for the union symbol. | ||
| 67 : | $BR | ||
| 68 : | |||
| 69 : | Increasing: \{ans_rule(35)\} | ||
| 70 : | $PAR | ||
| 71 : | EOT | ||
| 72 : | |||
| 73 : | @answers = (interval_cmp("(0,2*$a/3)")); | ||
| 74 : | gage | 268 | ANS(@answers ); |
| 75 : | jj | 62 | |
| 76 : | TEXT(EV2(<<EOT)); | ||
| 77 : | (C) Use interval notation to indicate where \( f(x) \) is decreasing. | ||
| 78 : | $BR | ||
| 79 : | Decreasing: \{ans_rule(35)\} | ||
| 80 : | $PAR | ||
| 81 : | EOT | ||
| 82 : | |||
| 83 : | @answers = (interval_cmp("(-Inf,0)U(2*$a/3,Inf)")); | ||
| 84 : | gage | 268 | ANS(@answers ); |
| 85 : | jj | 62 | |
| 86 : | TEXT(EV2(<<EOT)); | ||
| 87 : | (D) List the \(x\)-coordinates of all local maxima of \(f\). | ||
| 88 : | If there are no local maxima, enter 'NONE'. | ||
| 89 : | $BR | ||
| 90 : | \(x\) values of local maxima = \{ans_rule(20)\} | ||
| 91 : | $PAR | ||
| 92 : | EOT | ||
| 93 : | |||
| 94 : | gage | 268 | ANS(number_list_cmp( "2*$a/3" , strings=>["none"] )); |
| 95 : | jj | 62 | |
| 96 : | TEXT(EV2(<<EOT)); | ||
| 97 : | (E) List the \(x\)-coordinates of all local minima of \(f\). | ||
| 98 : | If there are no local minima, enter 'NONE'. | ||
| 99 : | $BR | ||
| 100 : | \(x\) values of local minima = \{ans_rule(20)\} | ||
| 101 : | $PAR | ||
| 102 : | EOT | ||
| 103 : | |||
| 104 : | gage | 268 | ANS(number_list_cmp( "0" , strings=>["none"] )); |
| 105 : | jj | 62 | |
| 106 : | TEXT(EV2(<<EOT)); | ||
| 107 : | (F) Use interval notation to indicate where \( f(x) \) is concave up. | ||
| 108 : | $BR | ||
| 109 : | Concave up: \{ans_rule(25)\} | ||
| 110 : | $PAR | ||
| 111 : | EOT | ||
| 112 : | |||
| 113 : | @answers = (interval_cmp("(-Inf,$a/3)")); | ||
| 114 : | gage | 268 | ANS(@answers ); |
| 115 : | jj | 62 | |
| 116 : | TEXT(EV2(<<EOT)); | ||
| 117 : | (G) Use interval notation to indicate where \( f(x) \) is concave down. | ||
| 118 : | $BR | ||
| 119 : | Concave down: \{ans_rule(35)\} | ||
| 120 : | $PAR | ||
| 121 : | EOT | ||
| 122 : | |||
| 123 : | @answers = (interval_cmp("($a/3,Inf)")); | ||
| 124 : | gage | 268 | ANS(@answers ); |
| 125 : | jj | 62 | |
| 126 : | TEXT(EV2(<<EOT)); | ||
| 127 : | (H)List the \(x \) values of all inflection points of \(f\). | ||
| 128 : | If there are no inflection points, enter 'NONE'. | ||
| 129 : | $BR | ||
| 130 : | \(x\) values of inflection points = \{ans_rule(20)\} | ||
| 131 : | $PAR | ||
| 132 : | EOT | ||
| 133 : | |||
| 134 : | gage | 268 | ANS(number_list_cmp( "$a/3" , strings=>["none"] )); |
| 135 : | jj | 62 | |
| 136 : | TEXT(EV2(<<EOT)); | ||
| 137 : | |||
| 138 : | (I) Use all of the preceding information to sketch a | ||
| 139 : | graph of \(f\). When you're finished, enter a "1" in the box | ||
| 140 : | below. | ||
| 141 : | $BR | ||
| 142 : | Graph Complete: \{ans_rule(12)\} | ||
| 143 : | $PAR | ||
| 144 : | EOT | ||
| 145 : | |||
| 146 : | @answers = (num_cmp(1) ); | ||
| 147 : | |||
| 148 : | gage | 268 | ANS(@answers ); |
| 149 : | jj | 62 | |
| 150 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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