#DESCRIPTION
#KEYWORDS('derivatives', 'critical points')
#ENDDESCRIPTION

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

loadMacros(
"PGcourse.pl",
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

###################
#
#  Setup

$a = non_zero_random(-9,9,1);
$b = non_zero_random(-5,5,1);
if (($a == $b) or (abs($b)==1)) { $b=-6; } 
$c = random(2,8,1);
if ($a == $c) { $c=9; } 

$ans = (- $a * $b - $c)/($b*$c);

###################
#
#  Text

BEGIN_TEXT

The function \( f(x) = ($c x+$a)e^{$b x} \)
has one critical number.  Find it. $BR
\{ans_rule(10) \}

END_TEXT

###################
#
#  Answer

ANS(num_cmp($ans));

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