##DESCRIPTION
## Max/min -- Find dimensions maximizing area of rectangle inscribed in ##parabola.
##ENDDESCRIPTION
##KEYWORDS('maximization,minimization', 'derivatives', 'maximum,minimum',
## 'optimization')

## Shotwell cleaned
## lcao , PAID on 11-24-2003

## DBsubject('Calculus')
## DBchapter('Applications of Differentiation')
## DBsection('Optimization Problems')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus: Early Transcendentals')
## EditionText1('6')
## AuthorText1('Stewart')
## Section1('4.7')
## Problem1('22')
DOCUMENT();        # This should be the first executable line in the problem.

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

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

$a=random(1,12,1);

BEGIN_TEXT
A rectangle is inscribed with its base on the \(x\)-axis and its
upper corners on the parabola \( y= $a-x^2\).  What are the dimensions of such a rectangle with the greatest possible area?
$BR$BR
Width = \{&ans_rule(15)\} Height = \{&ans_rule(15)\}
END_TEXT


ANS(num_cmp(["2*sqrt($a/3)","2*$a/3"], format=>"%0.5f", relTol=>1));

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