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# View of /trunk/NationalProblemLibrary/ASU-topics/setCalculus/stef/stef4_3p12.pg

Sat Sep 8 05:17:01 2007 UTC (5 years, 9 months ago) by sh002i
File size: 3287 byte(s)
Added tags for Rogawski's "Calculus: Early Transcendentals".


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