[npl] / branches / UGA / 5.2.3.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

View of /branches/UGA/5.2.3.pg

Sat Jul 24 17:09:50 2010 UTC (2 years, 10 months ago) by ted shifrin
File size: 1639 byte(s)
Log message

    1 ## DESCRIPTION
2 ##   Locate Critical Points
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Critical', 'Point', 'Partial', 'Multivariable')
6 ## Tagged by nhamblet
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Partial Derivatives')
10 ## DBsection('Maximum and Minimum Values')
11 ## Date('October 29, 2009')
12 ## Author('Shifrin')
13 ## Institution('UGA')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23   "PGstandard.pl",
24   "PGunion.pl",
25   "Parser.pl",
26   "parserVectorUtils.pl",
27   "PGcourse.pl"
28 );
29
30
31 TEXT(beginproblem());
32 BEGIN_PROBLEM();
33
34 ##############################################
35 #  Setup
36
37 Context("Vector");
38
39 #
40 #  The function
41 #
42 do{$c = non_zero_random(-5,5,1)} until ($c**2 != 1);
43 $a =$c**2 - 1;
44 $b = 3*$c**2;
45
46
47
48 $f = Formula("x^3 + 3*$a x y^2 - 3*$a y^2 -$b x")->reduce;
49 $arg = '\left(\begin{array}{c} x\\y \end{array}\right)'; 50 51 52 # 53 # Critical points 54 # 55$P1 = Point($c,0); 56$P2 = Point(-$c,0); 57$P3 = Point(1,1);
58 $P4 = Point(1,-1); 59 60 ############################################## 61 # Main text 62 63 Context()->texStrings; 64 BEGIN_TEXT 65 66 Find all the critical points of the function $$f arg=f$$. 67 68$PAR
69 List the points using ordered pair notation $$(a,b)$$, separated by commas.
70 $PAR 71 72$BCENTER
73 \{ans_rule(50)\}
74 $ECENTER 75 76 77 78 END_TEXT 79 Context()->normalStrings; 80 81 ################################################## 82 # Answers 83 84 ANS(List($P1,$P2,$P3,$P4)->cmp); 85 86$showPartialCorrectAnswers = 1;
87
88 ##################################################
89
90 END_PROBLEM();
91 ENDDOCUMENT();        # This should be the last executable line in the problem.


 aubreyja at gmail dot com ViewVC Help Powered by ViewVC 1.0.9