## DESCRIPTION
## Calculus
## ENDDESCRIPTION

## KEYWORDS('calculus','derivative','inflection point')
## Tagged by YL

## DBsubject('Calculus')
## DBchapter('Applications of Differentiation')
## DBsection('How Derivatives Affect the Shape of a Graph')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('Calculus: Early Transcendentals')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('4.3')
## Problem1('')

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

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

$a = random(2,8,1);
$b = random(2,8,1);

TEXT(beginproblem());

$showPartialCorrectAnswers = 1;

TEXT(EV2(<<EOT));
Consider the function
\[ f(x) = \frac{x}{$a x^2 ? {$b}}.  \]
$BR
List the \(x\) values of the inflection points of \(f\).
If there are no inflection points, enter 'NONE'.
$BR
 \{ans_rule(30)\}

EOT

ANS(number_list_cmp( "0,-sqrt(3*$b/$a),sqrt(3*$b/$a)" , strings=>["none"] ));


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