###########################################################
#
#  Example showing how to use the Parser's function
#  answer checker.
#

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
  "PGbasicmacros.pl",
  "PGanswermacros.pl",
  "Parser.pl",
  "Differentiation.pl",
);

TEXT(beginproblem());

###########################################################
#
#   The setup
#
Context('Vector')->variables->are(t=>'Real');

#
#   Define a function and its derivative and make them pretty
#
$a = random(1,8,1);
$b = random(-8,8,1);
$c = random(-8,8,1);

$f = Formula("<t^2,$at+$b,$c-t>") -> reduce;
$df = $f->D('t');

$t = random(-5,5,1);

###########################################################
#
#  The problem text
#

Context()->texStrings;
BEGIN_TEXT

Suppose \(f(t) = $f\).
$PAR
Then \(f'(t) =\) \{ans_rule(20)\},$BR
and \(f'($t) =\) \{ans_rule(20)\}.


END_TEXT
Context()->normalStrings;

###########################################################
#
#  The answers
#
ANS($df->cmp);
ANS($df->eval(t=>$t)->cmp);
$showPartialCorrectAnswers = 1;

###########################################################

ENDDOCUMENT();        # This should be the last executable line in the problem.