[npl] / trunk / NationalProblemLibrary / ASU-topics / setFirstDerivative / 4-2-29.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /trunk/NationalProblemLibrary/ASU-topics/setFirstDerivative/4-2-29.pg

Thu Jul 19 21:11:19 2007 UTC (5 years, 10 months ago) by jjholt
File size: 2292 byte(s)
Updated/Consolidated tags.


    1 ## DESCRIPTION
2 ## Information from the First Derivative
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('calculus', 'first derivative', 'critical points', 'minimum', 'maximum', 'increasing', 'decreasing')
6 ## Tagged by XW
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
26
27 DOCUMENT();        # This should be the first executable line in the problem.
28
30            "PGbasicmacros.pl",
31            "PGchoicemacros.pl",
33            "PGauxiliaryFunctions.pl",
35
36
37 $a = random(2,9,2); 38$b = non_zero_random(-9,9,2);
39
40 TEXT(beginproblem());
41
42 $showPartialCorrectAnswers = 1; 43 44 45 46 TEXT(EV2(<<EOT)); 47 Let 48 $f(x) = a x^3 ? {b}.$ 49$BR
50 (A) Use interval notation to indicate where $$f(x)$$ is increasing.
51 $PAR 52$PAR
53 $BBOLD Note:$EBOLD When using interval notation in WeBWorK, remember
54 that:
55 $BR 56 (i) You use 'I' for $$\infty$$ and '-I' for $$-\infty$$.$BR
57 (ii) 'U' for the union symbol.$BR 58 (iii) If the interval is empty, write "{}" without the quotation marks.$BR
59 $BR 60 61 Increasing: \{ans_rule(25)\} 62$PAR
63 $PAR 64 EOT 65 66 @answers = (interval_cmp("(-I,I)")); 67 68 ANS(@answers ); 69 70 TEXT(EV2(<<EOT)); 71$BR
72 (B) Use interval notation to indicate where $$f(x)$$ is decreasing.
73 $PAR 74 Decreasing: \{ans_rule(25)\} 75$PAR
76 $PAR 77 EOT 78 79 @answers = (str_cmp("{}") ); 80 81 ANS(@answers ); 82 83 TEXT(EV2(<<EOT)); 84$BR
85 (C) Find the average of the $$x$$ values of all local maxima of
86 $$f$$.
87 $BR 88 Note: If there are no local maxima, enter -1000. 89$PAR
90 Average of $$x$$ values = \{ans_rule(7)\}
91 $PAR 92$PAR
93 EOT
94
96
98
99 TEXT(EV2(<<EOT));
100 $BR 101 (D) Find the average of the $$x$$ values of all local minima of 102 $$f$$. 103$BR
104 Note: If there are no local minima, enter -1000.
105 $PAR 106 Average of $$x$$ values = \{ans_rule(7)\} 107$PAR
108 \$PAR
109 EOT
110