View of /trunk/NationalProblemLibrary/ma122DB/set9/s4_7_22.pg

    1 ##DESCRIPTION
    2 ## Max/min -- Find dimensions maximizing area of rectangle inscribed in ##parabola.
    3 ##ENDDESCRIPTION
    4 ##KEYWORDS('maximization,minimization', 'derivatives', 'maximum,minimum',
    5 ## 'optimization')
    6 
    7 ## Shotwell cleaned
    8 ## lcao , PAID on 11-24-2003
    9 
   10 ## DBsubject('Calculus')
   11 ## DBchapter('Applications of Differentiation')
   12 ## DBsection('Optimization Problems')
   13 ## Date('6/3/2002')
   14 ## Author('')
   15 ## Institution('')
   16 ## TitleText1('Calculus: Early Transcendentals')
   17 ## EditionText1('6')
   18 ## AuthorText1('Stewart')
   19 ## Section1('4.7')
   20 ## Problem1('22')
   21 DOCUMENT();        # This should be the first executable line in the problem.
   22 
   23 loadMacros("PGbasicmacros.pl",
   24            "PGanswermacros.pl",
   25 "PGauxiliaryFunctions.pl");
   26 
   27 TEXT(beginproblem());
   28 $showPartialCorrectAnswers=1;
   29 
   30 $a=random(1,12,1);
   31 
   32 BEGIN_TEXT
   33 A rectangle is inscribed with its base on the \(x\)-axis and its
   34 upper corners on the parabola \( y= $a-x^2\).  What are the dimensions of such a rectangle with the greatest possible area?
   35 $BR$BR
   36 Width = \{&ans_rule(15)\} Height = \{&ans_rule(15)\}
   37 END_TEXT
   38 
   39 
   40 ANS(num_cmp(["2*sqrt($a/3)","2*$a/3"], format=>"%0.5f", relTol=>1));
   41 
   42 ENDDOCUMENT();        # This should be the last executable line in the problem.