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| 1 : | sam | 2 | ##DESCRIPTION |
| 2 : | ##KEYWORDS('derivatives', 'tangent line') | ||
| 3 : | ## Find the derivatives of a polynomial evaluated at a point, use that to | ||
| 4 : | ## find the equation of the tangent line of the curve at that point | ||
| 5 : | ##ENDDESCRIPTION | ||
| 6 : | |||
| 7 : | DOCUMENT(); # This should be the first executable line in the problem. | ||
| 8 : | |||
| 9 : | loadMacros( | ||
| 10 : | "PG.pl", | ||
| 11 : | "PGbasicmacros.pl", | ||
| 12 : | "PGchoicemacros.pl", | ||
| 13 : | "PGanswermacros.pl", | ||
| 14 : | "PGauxiliaryFunctions.pl" | ||
| 15 : | ); | ||
| 16 : | |||
| 17 : | TEXT(&beginproblem); | ||
| 18 : | $showPartialCorrectAnswers = 1; | ||
| 19 : | |||
| 20 : | $a1 = random(2,5,1); | ||
| 21 : | $b1 = random(2,3,1); | ||
| 22 : | $c1 = random(2,7,1); | ||
| 23 : | $d1 = random(2,6,1); | ||
| 24 : | $n1 = random(3,7,1); | ||
| 25 : | $x1 = random(4,5,1); | ||
| 26 : | $y1 = $a1*$x1+$b1* $x1**.5; | ||
| 27 : | $m1 = $a1+(.5)*$b1*$x1**(-.5); | ||
| 28 : | |||
| 29 : | TEXT(EV2(<<EOT)); | ||
| 30 : | If \( f(x) = $a1 x + $b1 \sqrt{ x} \), find \( f'( $x1 ) \). | ||
| 31 : | $BR $BR \{ans_rule(20) \} | ||
| 32 : | $BR | ||
| 33 : | EOT | ||
| 34 : | |||
| 35 : | $ans = $m1; | ||
| 36 : | &ANS(std_num_cmp($ans)); | ||
| 37 : | |||
| 38 : | TEXT(EV2(<<EOT)); | ||
| 39 : | Use this to find the equation of the tangent line to the curve | ||
| 40 : | \( y = $a1 x + $b1 \sqrt{ x} \) | ||
| 41 : | at the point \( ( $x1 , !{$y1:%.5f} ) \). | ||
| 42 : | The equation of this tangent line can be written in the form \( y = mx+b \) | ||
| 43 : | where \( m \) is: \{ans_rule(20) \} | ||
| 44 : | $BR | ||
| 45 : | EOT | ||
| 46 : | $ans = $m1; | ||
| 47 : | &ANS(std_num_cmp($ans)); | ||
| 48 : | |||
| 49 : | TEXT(EV2(<<EOT)); | ||
| 50 : | and where \( b \) is: \{ans_rule(20) \} | ||
| 51 : | $BR | ||
| 52 : | EOT | ||
| 53 : | $ans = $y1 -$m1*$x1; | ||
| 54 : | &ANS(std_num_cmp($ans)); | ||
| 55 : | |||
| 56 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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