View of /trunk/NationalProblemLibrary/ma122DB/set5/s3_5_7.pg

    1 ##DESCRIPTION
    2 ##  Find a derivative of a polynomial; requires use of chain rule
    3 ##ENDDESCRIPTION
    4 ##KEYWORDS('derivatives', 'chain rule')
    5 
    6 ## Shotwell cleaned
    7 ## tcao , PAID on 11-24-2003
    8 
    9 ## DBsubject('Calculus')
   10 ## DBchapter('Differentiation')
   11 ## DBsection('The Chain Rule')
   12 ## Date('6/3/2002')
   13 ## Author('')
   14 ## Institution('')
   15 ## TitleText1('Calculus: Early Transcendentals')
   16 ## EditionText1('6')
   17 ## AuthorText1('Stewart')
   18 ## Section1('3.4')
   19 ## Problem1('7')
   20 
   21 
   22 DOCUMENT();        # This should be the first executable line in the problem.
   23 
   24 loadMacros(
   25 "PGbasicmacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a1 = random(2,5,1);
   34 $b1 = random(2,8,1);
   35 $c1 = random(2,4,1);
   36 $x1 = random(1,5,1);
   37 $deriv1 = "($c1*($x1^3+$a1*$x1+$b1)^($c1-1))*(3*$x1*$x1+$a1)";
   38 $funct1 = "($c1*(x^3+$a1*x+$b1)^($c1-1))*(3*x*x+$a1)";
   39 
   40 BEGIN_TEXT
   41 Let \[ f(x) = (x^3+ $a1 x + $b1) ^ { $c1 } \]
   42 $BR
   43 \( f'( x ) = \) \{ans_rule(40) \}
   44 
   45 $BR
   46 \( f'( $x1 ) = \) \{ans_rule(40) \}
   47 $BR
   48 END_TEXT
   49 
   50 ANS(fun_cmp($funct1));
   51 ANS(num_cmp($deriv1));
   52 
   53 ENDDOCUMENT();        # This should be the last executable line in the problem.