View of /trunk/rochester_problib/setDerivatives1/nsc2s10p3.pg

    1 #DESCRIPTION
    2 # Identify the graphs of the function and the derivative
    3 #ENDDESCRIPTION
    4 
    5 #KEYWORDS('derivatives', 'graphs')
    6 
    7 DOCUMENT();        # This should be the first executable line in the problem.
    8 
    9 loadMacros(
   10 "PG.pl",
   11 "PGbasicmacros.pl",
   12 "PGchoicemacros.pl",
   13 "PGanswermacros.pl",
   14 "PGauxiliaryFunctions.pl",
   15 "PGgraphmacros.pl"
   16 );
   17 
   18 TEXT(&beginproblem);
   19 $showPartialCorrectAnswers = 1;
   20 
   21 $a=random(0, 6.3, .1);
   22 $b=random(.7, .9, .1);
   23 
   24 $dom = 4;
   25 @slice = NchooseK(3,3);
   26 
   27 @colors = ("blue", "red", "green");
   28 @sc = @colors[@slice];  #scrambled colors
   29 @sa = ('A','B','C')[@slice];
   30 
   31 # define the functions and their derivatives.
   32 # FEQ (Format EQuations) cleans up the writing of the functions (see FEQ in PGbasicmacros)
   33 # Otherwise we would need to worry about the signs of $a, $b and so forth.
   34 
   35 $f = FEQ("sin($a+$b*cos(x)) for x in <-$dom,$dom> using color:$sc[0] and weight:2");
   36 $fp = FEQ("cos($a+$b*cos(x))*(-$b)*sin(x)   for x in <-$dom,$dom> using color=$sc[1] and weight:2");
   37 $fpp = FEQ("-sin($a+$b*cos(x))*$b*$b*sin(x)*sin(x)+ cos($a+$b*cos(x))*(-$b)*cos(x) for x in <-$dom,$dom> using color=$sc[2] and weight=2");
   38 
   39 $graph = init_graph(-4,-4,4,4,'axes'=>[0,0],'grid'=>[8,8]);
   40 
   41 ($fRef,$fpRef,$fppRef) = plot_functions( $graph,
   42                $f,$fp,$fpp
   43                            );
   44 
   45         # create labels
   46 
   47 $label_point=-1;
   48 $label_f = new Label ( $label_point,&{$fRef->rule}($label_point),$sa[0],"$sc[0]",'left')        ;
   49         # NOTE: $fRef->rule is a reference to the subroutine which calculates the
   50         # function.  It was defined in the output of plot_functions. It is used         here
   51         # to calculate the y value of the label corresponding to the function,
   52         # and below to find the y values for the labels corresponding to the
   53         # first and second derivatives.
   54 
   55 $label_fp = new Label ( $label_point+.5,&{$fpRef->rule}($label_point+.5),$sa[1],"$sc[1]",'left')      ;
   56 $label_fpp = new Label ( $label_point+1,&{$fppRef->rule}($label_point+1),$sa[2],"$sc[2]",'left');
   57 
   58         # insert the labels into the graph
   59 $graph->lb($label_f,$label_fp,$label_fpp);
   60 
   61 TEXT(image(insertGraph($graph)));
   62 TEXT(EV2(qq!
   63 Identify the graphs A (blue), B( red) and C (green) as the graphs of a function and its
   64 derivatives:$PAR
   65 \{ans_rule(4)\} is the graph of the function $PAR
   66 \{ans_rule(4)\} is the graph of the function's first derivative $PAR
   67 \{ans_rule(4)\} is the graph of the function's second derivative $PAR
   68 !));
   69 &ANS(str_cmp( [ @sa ] ) );
   70 
   71 ENDDOCUMENT();        # This should be the last executable line in the problem.
   72