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| Rev | Author | Line No. | Line |
|---|---|---|---|
| 6509 | bpr | 1 | \title{Tangente 3} |
| 2 | \range{-5,5} |
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| 3 | \real{a = random(-1,1)*randint(1..30)/10} |
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| 4 | \real{b = randint(-20..20)/10} |
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| 5 | \real{c = randint(-20..20)/10} |
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| 6 | \function{f = \a*x^2+simplify(\b*x) + \c} |
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| 7 | \real{x0 = randint(-40..40)/10} |
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| 8 | \real{y0 = evalue(\f, x = \x0)} |
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| 9 | \function{df = diff(\f,x)} |
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| 10 | \real{df0 = evalue(\df,x = \x0)} |
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| 11 | \function{D = \df0*x - simplify(\df0*\x0 - \y0)} |
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| 12 | \integer{xmin = min(-3, \x0 - 2)} |
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| 13 | \integer{xmax = max(3, \x0 + 2)} |
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| 8514 | bpr | 14 | \text{A = slib(function/bounds \f, x,\xmin,\xmax)} |
| 6509 | bpr | 15 | \integer{ymin = min(-3, \A[1] - 2)} |
| 16 | \integer{ymax = max(3, \A[2] + 2)} |
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| 17 | \text{rangex = \xmin, \xmax} |
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| 18 | \text{rangey = \ymin, \ymax} |
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| 184 | bpr | 19 | |
| 6509 | bpr | 20 | \text{dessin = rangex \rangex |
| 21 | rangey \rangey |
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| 22 | arrow \xmin,0,\xmax,0,10, black |
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| 23 | arrow 0,\ymin,0,\ymax,10, black |
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| 24 | plot navy,\f |
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| 25 | circle \x0,\y0,5, red |
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| 26 | text black,0,0,roman,0 |
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| 27 | } |
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| 28 | \text{url = draw(200,200 |
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| 29 | \dessin)} |
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| 30 | \text{dessinc = \dessin |
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| 31 | plot green,\D |
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| 32 | } |
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| 33 | \text{urlc = draw(200,200 |
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| 34 | \dessinc)} |
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| 35 | \real{x1 = \x0+1} |
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| 36 | \real{y1 = \df0*\x1 - \df0*\x0 + \y0} |
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| 37 | \text{P0 = slib(draw/convpixel \x0,\y0,200,200,\rangex,\rangey,0,pixels)} |
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| 38 | \text{P1 = slib(draw/convpixel \x1,\y1,200,200,\rangex,\rangey,0,pixels)} |
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| 39 | \text{rep = \url;line,\P0[1],\P0[2],\P1[1],\P1[2]} |
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| 184 | bpr | 40 | |
| 8514 | bpr | 41 | \statement{En utilisant la souris, positionner la tangente |
| 6509 | bpr | 42 | à la courbe d'équation \(y = \f\) au point d'abscisse \x0. |
| 8514 | bpr | 43 | <div class="wims_instruction"> |
| 44 | NB : le tracé sera obtenu en définissant deux points |
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| 45 | appartenant à cette tangente. |
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| 46 | </div> |
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| 47 | <div class="wimscenter">\embed{reply1,200x200}</div> |
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| 184 | bpr | 48 | } |
| 14019 | bpr | 49 | \answer{}{\rep}{type=jsxgraphcurve} |
| 6509 | bpr | 50 | |
| 51 | \text{dessinc = \dessin |
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| 52 | plot green,\D |
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| 184 | bpr | 53 | } |
| 8514 | bpr | 54 | \solution{La droite tangente au point d'abscisse \x0 est dessinée en vert : |
| 17280 | bpr | 55 | <p class="wimscenter"><img src="\urlc" alt=""></p> |
| 6509 | bpr | 56 | } |