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# View of /trunk/NationalProblemLibrary/Rochester/setVmultivariable7MaxMin/ur_vc_7_13.pg

Wed Jun 27 19:34:12 2007 UTC (5 years, 10 months ago) by jjholt
File size: 1090 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());
32
33 \$a = random(2, 9, 1);
34 \$b = random(2, 9, 1);
35
36 BEGIN_TEXT
37 Find the maximum and minimum values of  \( f(x, y) = xy \) on the ellipse
38 \( \$a\!x^{2} + y^{2} = \$b \).
39 \$BR
40 maximum value = \{ ans_rule(20) \}\$BR
41 minimum value = \{ ans_rule(20) \}
42 END_TEXT
43
44 ANS(num_cmp( .5*\$b/sqrt(\$a) ) );
45 ANS(num_cmp( - .5*\$b/sqrt(\$a) ) );
46
47 ENDDOCUMENT();    # This should be the last executable line in the problem.
```