[npl] / trunk / NationalProblemLibrary / Rochester / setVmultivariable7MaxMin / ur_vc_7_2.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /trunk/NationalProblemLibrary/Rochester/setVmultivariable7MaxMin/ur_vc_7_2.pg

Wed Jun 27 19:34:12 2007 UTC (5 years, 10 months ago) by jjholt
File size: 1219 byte(s)
Updated/Corrected tags.  --JJH


    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('critical points' 'minimum' 'maximum' 'multivariable')
6 ## Tagged by tda2d
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Partial Derivatives')
10 ## DBsection('Maximum and Minimum Values')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20
21 DOCUMENT();   # This should be the first executable line in the problem.
22
24            "PGbasicmacros.pl",
25            "PGchoicemacros.pl",
27            "PGauxiliaryFunctions.pl"
28           );
29
30 TEXT(beginproblem());
31 $showPartialCorrectAnswers = 1; 32 33 BEGIN_TEXT 34 Suppose $$f(x, y) = xy - ax - by$$. 35$PAR
36 (A) How many local minimum points does $$f$$ have in $$\mathbf{R}^{2}$$?  (The
37 answer is an integer).$BR 38 \{ ans_rule(5) \} 39$PAR
40 (B) How many local maximum points does $$f$$ have in $$\mathbf{R}^{2}$$?$BR 41 \{ ans_rule(5) \} 42$PAR
43 (C) How many saddle points does $$f$$ have in $$\mathbf{R}^{2}$$?\$BR
44 \{ ans_rule(5) \}
45 END_TEXT
46
47 ANS(num_cmp(0) );
48 ANS(num_cmp(0) );
49 ANS(num_cmp(1) );
50
51
52 ENDDOCUMENT();    # This should be the last executable line in the problem.