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# Diff of /trunk/NationalProblemLibrary/Rochester/setDerivatives12MVT/c3s2p1.pg

Revision 3023 Revision 3024
9## DBchapter('Applications of Differentiation') 9## DBchapter('Applications of Differentiation')
10## DBsection('The Mean Value Theorem') 10## DBsection('The Mean Value Theorem')
11## Date('') 11## Date('')
12## Author('') 12## Author('')
13## Institution('Rochester') 13## Institution('Rochester')
14## TitleText1('') 14## TitleText1('Calculus: Early Transcendentals')
15## EditionText1('') 15## EditionText1('6')
16## AuthorText1('') 16## AuthorText1('Stewart')
17## Section1('') 17## Section1('4.2')
18## Problem1('') 18## Problem1('12')
19
19 20
20DOCUMENT(); # This should be the first executable line in the problem. 21DOCUMENT(); # This should be the first executable line in the problem.
21 22
22loadMacros("PG.pl", 23loadMacros("PG.pl",
23 "PGbasicmacros.pl", 24 "PGbasicmacros.pl",
47 \$b=2*\$A2; 48 \$b=2*\$A2;
48 \$c = \$A1 - \$avg; 49 \$c = \$A1 - \$avg;
49 \$discrim = \$b**2 - 4*\$a*\$c; 50 \$discrim = \$b**2 - 4*\$a*\$c;
50 } 51 }
51 52
53\$poly = nicestring([\$A3, \$A2, \$A1, \$A0]);
54
52\$root1 = ( -\$b - sqrt(\$discrim) ) /(2*\$a); 55\$root1 = ( -\$b - sqrt(\$discrim) ) /(2*\$a);
53\$root2 = ( -\$b + sqrt(\$discrim) ) /(2*\$a); 56\$root2 = ( -\$b + sqrt(\$discrim) ) /(2*\$a);
54TEXT(EV2(<<EOT)); 57TEXT(EV2(<<EOT));
55Consider the function 58Consider the function
56\[ f(x) = !{\$A3}x^3 ? {\$A2}x^2 ? {\$A1}x ? {\$A0} \] 59\[ f(x) = \$poly\]
57Find the average slope of this function on the interval \( ( \$left , \$right ) \). 60Find the average slope of this function on the interval \( ( \$left , \$right ) \).
58\{ans_rule(20) \} \$BR 61\{ans_rule(20) \} \$BR
59EOT 62EOT
60 63
61if (\$left<= \$root1 and \$root1 <= \$right and \$left < \$root2 and \$root2 <= \$right) { # both roots are in interval) 64if (\$left<= \$root1 and \$root1 <= \$right and \$left < \$root2 and \$root2 <= \$right) { # both roots are in interval)

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