Problem4

Prep Main Page > Web Conference 2 > Sample Problems > Problem 4

This is Library/ASU-topics/setSecondDerivative/4-3-77.pg

## DESCRIPTION
## Calculus: Second Derivatives
## ENDDESCRIPTION

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

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

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

TEXT(beginproblem());

$showPartialCorrectAnswers = 1;

TEXT(EV2(<<EOT));
Suppose that
\[ f(x) = \frac{x}{$a x^2 ? {$b}}.  \]
$BR
$BR
(A) Find the $BBOLD average $EBOLD of the $BBOLD two smallest $EBOLD inflection points of \(f\).
$PAR
Average of two smallest inflection points = \{ans_rule(20)\}
$BR
$BR
(B) Find the $BBOLD average $EBOLD of the $BBOLD two largest $EBOLD inflection points of \(f\).
$PAR
Average of two largest inflection points = \{ans_rule(20)\}

EOT

@answers = ( num_cmp(-sqrt(3*$b/($a))/2), num_cmp(sqrt(3*$b/($a))/2));

ANS(@answers );

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