DifferentiateFunction1

Differentiating and Evaluating a Function

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This PG code shows how to create a function using MathObjects, differentiate it, and evaluate it.

• Download file: File:DifferentiateFunction1.txt (change the file extension from txt to pg when you save it)
• File location in NPL: FortLewis/Authoring/Templates/DiffCalc/DifferentiateFunction1.pg

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PG problem file	Explanation
Problem tagging data	Problem tagging:
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "AnswerFormatHelp.pl", "unionLists.pl", ); TEXT(beginproblem());	Initialization: We load unionLists.pl to create an enumerated list in the Main Text section.
Context("Numeric")->variables->add(k=>"Real"); Context()->flags->set( reduceConstants=>0, # no decimals reduceConstantFunctions=>1, # combine 4+5*2? formatStudentAnswer=>'parsed', # no decimals ); $a = random(6,9,1); $k = random(3,5,1); $f = Formula("k x^2"); $fx = $f->D('x'); @answer = (); $answer[0] = $fx; $answer[1] = $fx->substitute(k=>$k); $answer[2] = $fx->substitute(x=>$a*pi,k=>$k);	Setup: The partial differentiation operator is ->D('x'). The main difference between eval() and substitute() is eval() returns a Real (a number) substitute() returns a Formula Since plugging a particular number $k into the Formula $f returns a Formula $k x, if we had used the eval method $answer[1] = $fx->eval(k=>$k); instead of the substitute method, we would get errors because $k x is a Formula, not a Real. When the answer is a constant, we can use either the eval method, in which case the answer would be a Real, or the substitute method, in which case the answer would be a constant Formula. If you use the eval method, $answer[2] = $fx->eval(x=>$a*pi,k=>$k); the answer will be a Real and will display as a single number in decimal format. If you use the substitute method instead, you have more control over how the answer will be displayed. In particular, the context flag reduceConstants=>0 controls whether the answer will be reduced to a single number in decimal format, the flag reduceConstantFunctions=>1 controls whether or not expressions such as 4+5*2 are reduced to 14, and setting the context flag formatStudentAnswer=>'parsed' will prevent the student's answer from being reduced to a single number in decimal format and will also display pi instead of 3.14159... Setting the context flag reduceConstants=>1 would reduce answers to decimals, and setting it to zero does not evaluate to decimals.
Context()->texStrings; BEGIN_TEXT Suppose \( f(x) = $f \) where \( k \) is a constant. \{ BeginList("OL",type=>"a") \} $ITEM \( f'(x) = \) \{ ans_rule(20) \} \{ AnswerFormatHelp("formulas") \} $ITEM If \( k = $k \) then \( f'(x) = \) \{ ans_rule(20) \} \{ AnswerFormatHelp("formulas") \} $ITEM If \( k = $k \) then \( f'($a\pi) = \) \{ ans_rule(20) \} \{ AnswerFormatHelp("formulas") \} \{ EndList("OL") \} END_TEXT Context()->normalStrings;	Main Text:
$showPartialCorrectAnswers = 1; foreach my $i (0..2) { ANS( $answer[$i]->cmp() ); }	Answer Evaluation:
Context()->texStrings; BEGIN_SOLUTION ${PAR}SOLUTION:${PAR} Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT("MathObject version."); ENDDOCUMENT();	Solution:

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