##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.