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| 1 : | jj | 61 | ## DESCRIPTION |
| 2 : | ## Calculus | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ## KEYWORDS('Calculus', 'Single Variable','derivative') | ||
| 6 : | ## Tagged by LD | ||
| 7 : | |||
| 8 : | ## DBsubject('Calculus') | ||
| 9 : | ## DBchapter('Single Variable') | ||
| 10 : | ## DBsection('Differentiation') | ||
| 11 : | ## Date('') | ||
| 12 : | ## Author('') | ||
| 13 : | ## Institution('ASU') | ||
| 14 : | ## TitleText1('') | ||
| 15 : | ## EditionText1('') | ||
| 16 : | ## AuthorText1('') | ||
| 17 : | ## Section1('') | ||
| 18 : | ## Problem1('') | ||
| 19 : | |||
| 20 : | DOCUMENT(); | ||
| 21 : | |||
| 22 : | loadMacros( | ||
| 23 : | "PG.pl", | ||
| 24 : | "PGbasicmacros.pl", | ||
| 25 : | "PGchoicemacros.pl", | ||
| 26 : | "PGanswermacros.pl", | ||
| 27 : | "PGauxiliaryFunctions.pl" | ||
| 28 : | ); | ||
| 29 : | |||
| 30 : | TEXT(&beginproblem); | ||
| 31 : | $showpartialcorrectanswers = 1; | ||
| 32 : | |||
| 33 : | $a = random(2, 13, 1); | ||
| 34 : | $b = random(2,7,1); | ||
| 35 : | $c = random(2,7,1); | ||
| 36 : | $d = random(3,9,1); | ||
| 37 : | $r1 = random(1,12,1); | ||
| 38 : | $r2 = random(-12,-1,1); | ||
| 39 : | |||
| 40 : | TEXT(EV2(<<EOT)); | ||
| 41 : | Let \( f(x) = ($a x^2 + $b x)($c x - $d) \). | ||
| 42 : | Evaluate \( f'(x) \) at the following points: | ||
| 43 : | $BR | ||
| 44 : | (A) \( f'($r1)\) = \{ans_rule(40) \} | ||
| 45 : | $BR | ||
| 46 : | $BR | ||
| 47 : | EOT | ||
| 48 : | |||
| 49 : | $ans = (2*$a*($r1) + $b)*($c*(($r1)) - $d) + ($a*(($r1)**2) + $b*($r1))*($c); | ||
| 50 : | &ANS(std_num_cmp($ans)); | ||
| 51 : | |||
| 52 : | TEXT(EV2(<<EOT)); | ||
| 53 : | (B) \( f'($r2) \) = \{ ans_rule(40) \} | ||
| 54 : | $BR | ||
| 55 : | EOT | ||
| 56 : | |||
| 57 : | $ans = (2*$a*($r2) + $b)*($c*(($r2)) - $d) + ($a*(($r2)**2) + $b*($r2))*($c); | ||
| 58 : | &ANS(std_num_cmp($ans)); | ||
| 59 : | |||
| 60 : | ENDDOCUMENT(); |
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