## DESCRIPTION
## Calculus
## ENDDESCRIPTION

## KEYWORDS('tangent' 'slope')
## Tagged by tda2d

## DBsubject('Calculus')
## DBchapter('Partial Derivatives')
## DBsection('Directional Derivatives and the Gradient Vector')
## Date('')
## Author('')
## Institution('Dartmouth')
## TitleText1('Basic Multivariable Calculus')
## EditionText1('3')
## AuthorText1('Marsden, Tromba, Weinstein')
## Section1('2.6')
## Problem1('')

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

## Do NOT show partial correct answers
$showPartialCorrectAnswers = 1;

## Lots of set up goes here
$x1 = random(1,8,1);
$y1 = random(1,8,1);

$a = random(1,4,1);
$a_x = clean_scalar_string($a, "x");

$b = random(1,4,1);
$b_y = clean_scalar_string($b, "y");

$c = random(1,4,1);
$c_xy = clean_scalar_string($c, "xy");

#$d = sqrt($a*$x1+$b*$y1) + sqrt($c*$x1*$y1);

$num = $a/(2*sqrt($a*$x1 + $b*$y1) ) + $c*$y1/(2*sqrt($c*$x1*$y1) );
$denom = $b/(2*sqrt($a*$x1+$b*$y1) ) + $c*$x1/(2*sqrt($c*$x1*$y1) );

$yp = - $num/$denom;

#
## Ok, we are ready to begin the problem...
##
TEXT(beginproblem());


BEGIN_TEXT
$BR
Find the slope of the tangent line to the curve
$BR
\(\displaystyle \sqrt{$a_x +$b_y}  + \sqrt{$c_xy} = 
    \sqrt{\{$a*$x1+$b*$y1\}} + \sqrt{\{$c*$x1*$y1\}} \)
at the point \( ( $x1,$y1 ) \). $BR

The slope is \{ ans_rule(70) \}.

END_TEXT

ANS(num_cmp($yp));
ENDDOCUMENT();