View of /trunk/NationalProblemLibrary/ma122DB/set8/s4_3_64.pg

    1 ##DESCRIPTION
    2 ## Determine concavity
    3 ## ENDDESCRIPTION
    4 ##KEYWORDS('derivatives', 'concave upward')
    5 
    6 ## Shotwell cleaned
    7 ## lcao , PAID on 11-24-2003
    8 
    9 ## DBsubject('Calculus')
   10 ## DBchapter('Applications of Differentiation')
   11 ## DBsection('How Derivatives Affect the Shape of a Graph')
   12 ## Date('6/3/2002')
   13 ## Author('')
   14 ## Institution('')
   15 ## TitleText1('Calculus: Early Transcendentals')
   16 ## EditionText1('6')
   17 ## AuthorText1('Stewart')
   18 ## Section1('4.3')
   19 ## Problem1('64')
   20 ## TitleText2('Calculus: Early Transcendentals')
   21 ## EditionText2('1')
   22 ## AuthorText2('Rogawski')
   23 ## Section2('4.4')
   24 ## Problem2('61')
   25 
   26 
   27 DOCUMENT();        # This should be the first executable line in the problem.
   28 
   29 loadMacros(
   30 "PGbasicmacros.pl",
   31 "PGanswermacros.pl",
   32 "PGauxiliaryFunctions.pl"
   33 );
   34 
   35 TEXT(beginproblem());
   36 $showPartialCorrectAnswers = 0;
   37 
   38 BEGIN_TEXT
   39 Suppose that on the interval \(I\), \(f(x)\) is positive and concave up. Furthermore, assume that \(f''(x)\) exists and let \(g(x)=(f(x))^2\). Use this information to answer the following questions. $BR$BR
   40 
   41 $BR$BR To answer the questions, choose your answers from the following list: $BR$BR
   42 
   43  $BCENTER $BITALIC CU $EITALIC (concave up), $BITALIC CD $EITALIC (concave down), $BITALIC f(x) $EITALIC , $BITALIC f'(x) $EITALIC , $BITALIC f''(x) $EITALIC, $BITALIC 0 $EITALIC, or $BITALIC 1 $EITALIC. $ECENTER
   44 $BR$BR
   45 
   46 $BBOLD a.) $EBOLD \(f''(x) > \) \{ans_rule(10) \} on \(I\). $BR$BR
   47 $BBOLD b.) $EBOLD  \(g''(x)=2(A^2+B\,f''(x)) \), where
   48  \(A=\)  \{ans_rule(10) \} and \(B=\)  \{ans_rule(10) \}. $BR$BR
   49 $BBOLD c.) $EBOLD \(g''(x) > \)  \{ans_rule(10) \} on \(I\). $BR$BR
   50 $BBOLD d.) $EBOLD \(g(x) \) is  \{ans_rule(10) \} on \(I\).
   51 
   52 END_TEXT
   53 
   54 $ans1 = 0;
   55 $ans2 = "f'(x)";
   56 $ans3 = "f(x)";
   57 $ans4 = 0;
   58 $ans5 = "CU";
   59 ANS(num_cmp($ans1));
   60 ANS(str_cmp($ans2));
   61 ANS(str_cmp($ans3));
   62 ANS(num_cmp($ans4));
   63 ANS(str_cmp($ans5));
   64 ENDDOCUMENT();        # This should be the last executable line in the problem.