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{"version":3,"file":"can2F18-wA2reqNh.js","sources":["../../src/exercices/can/2e/can2F18.js"],"sourcesContent":["import { repere } from '../../../lib/2d/reperes.js'\nimport { texteParPosition } from '../../../lib/2d/textes.js'\nimport { spline } from '../../../lib/mathFonctions/Spline.js'\nimport { choice } from '../../../lib/outils/arrayOutils'\nimport { mathalea2d } from '../../../modules/2dGeneralites.js'\nimport { randint } from '../../../modules/outils.js'\nimport { miseEnEvidence } from '../../../lib/outils/embellissements'\nimport Exercice from '../../Exercice.js'\nexport const dateDePublication = '16/11/2023'\nexport const interactifReady = true\nexport const interactifType = 'mathLive'\nexport const titre = 'Déterminer un extremum graphiquement'\n\n/*!\n * @author Gilles MORA\n *\n * Référence can2F18\n*/\nexport const uuid = '5a908'\nexport const ref = 'can2F18'\nexport default function MaxMinG () {\n Exercice.call(this)\n this.typeExercice = 'simple'\n this.nbQuestions = 1\n this.tailleDiaporama = 1\n this.formatChampTexte = 'largeur15 inline lycee nospacebefore'\n this.nouvelleVersion = function () {\n const noeuds1 = [{ x: -4, y: -1, deriveeGauche: 0, deriveeDroit: 0, isVisible: true },\n { x: -3, y: 0, deriveeGauche: 1, deriveeDroit: 1, isVisible: true },\n { x: -2, y: 1, deriveeGauche: 0, deriveeDroit: 0, isVisible: true },\n { x: -1, y: 0, deriveeGauche: -1, deriveeDroit: -1, isVisible: true },\n { x: 0, y: -1, deriveeGauche: -1, deriveeDroit: -1, isVisible: true },\n { x: 2, y: -2, deriveeGauche: -1, deriveeDroit: -1, isVisible: true },\n { x: 3, y: -3, deriveeGauche: 0, deriveeDroit: 0, isVisible: true },\n { x: 4, y: -2, deriveeGauche: 1, deriveeDroit: 1, isVisible: true },\n { x: 5, y: -1, deriveeGauche: 0, deriveeDroit: 0, isVisible: true }\n ]\n const noeuds2 = [{ x: -4, y: 0, deriveeGauche: 0, deriveeDroit: 0, isVisible: true },\n { x: -3, y: 1, deriveeGauche: 1, deriveeDroit: 1, isVisible: true },\n { x: -2, y: 3, deriveeGauche: 0, deriveeDroit: 0, isVisible: true },\n { x: -1, y: 1, deriveeGauche: -1, deriveeDroit: -1, isVisible: true },\n { x: 0, y: 0, deriveeGauche: -1, deriveeDroit: -1, isVisible: true },\n { x: 2, y: -1, deriveeGauche: 0, deriveeDroit: 0, isVisible: true },\n { x: 3, y: 0, deriveeGauche: 2, deriveeDroit: 2, isVisible: true },\n { x: 4, y: 1, deriveeGauche: 0, deriveeDroit: 0, isVisible: true },\n { x: 5, y: 0, deriveeGauche: -1, deriveeDroit: -1, isVisible: true },\n { x: 6, y: -2, deriveeGauche: 0, deriveeDroit: 0, isVisible: true }\n ]\n const noeuds3 = [{ x: -4, y: -3, deriveeGauche: 0, deriveeDroit: 0, isVisible: true },\n { x: -3, y: -2, deriveeGauche: 1, deriveeDroit: 1, isVisible: true },\n { x: -2, y: 0, deriveeGauche: 2, deriveeDroit: 2, isVisible: true },\n { x: -1, y: 2, deriveeGauche: 1, deriveeDroit: 1, isVisible: true },\n { x: 0, y: 3, deriveeGauche: 0, deriveeDroit: 0, isVisible: true },\n { x: 2, y: 2, deriveeGauche: -1, deriveeDroit: -1, isVisible: true },\n { x: 4, y: 0, deriveeGauche: 0, deriveeDroit: 0, isVisible: true },\n { x: 5, y: 2, deriveeGauche: 2, deriveeDroit: 2, isVisible: true }\n ]\n const mesFonctions = [noeuds3, noeuds1, noeuds2]//\n function aleatoiriseCourbe (listeFonctions) {\n const coeffX = choice([-1, 1]) // symétries ou pas\n const coeffY = choice([-1, 1])\n const deltaX = randint(-2, +2) // translations\n const deltaY = randint(-1, 1)// randint(-2, +2)\n const choix = choice(listeFonctions)\n return choix.map((noeud) => Object({\n x: (noeud.x + deltaX) * coeffX,\n y: (noeud.y + deltaY) * coeffY,\n deriveeGauche: noeud.deriveeGauche * coeffX * coeffY,\n deriveeDroit: noeud.deriveeDroit * coeffX * coeffY,\n isVisible: noeud.isVisible\n }))\n }\n let bornes = {}\n const o = texteParPosition('O', -0.3, -0.3, 'milieu', 'black', 1)\n const nuage = aleatoiriseCourbe(mesFonctions)\n const theSpline = spline(nuage)\n this.spline = theSpline\n bornes = theSpline.trouveMaxes()\n const repere1 = repere({\n xMin: bornes.xMin - 1,\n xMax: bornes.xMax + 1,\n yMin: bornes.yMin - 1,\n yMax: bornes.yMax + 1,\n grilleX: false,\n grilleY: false,\n grilleSecondaire: true,\n grilleSecondaireYDistance: 1,\n grilleSecondaireXDistance: 1,\n grilleSecondaireYMin: bornes.yMin - 1,\n grilleSecondaireYMax: bornes.yMax + 1,\n grilleSecondaireXMin: bornes.xMin - 1,\n grilleSecondaireXMax: bornes.xMax + 1\n })\n const courbe1 = theSpline.courbe({\n repere: repere1,\n epaisseur: 1.5,\n ajouteNoeuds: true,\n optionsNoeuds: { color: 'blue', taille: 2, style: 'x', epaisseur: 2 },\n color: 'blue'\n })\n const objetsEnonce = [repere1, courbe1]\n const solsMax = theSpline.solve(Math.max(...nuage.map(el => el.y)))\n const solsMin = theSpline.solve(Math.min(...nuage.map(el => el.y)))\n const choix = choice([true, false])\n this.reponse = choix ? Math.max(...nuage.map(el => el.y)) : Math.min(...nuage.map(el => el.y))\n this.question = `On donne la représentation graphique d'une fonction $f$. <br>\n Déterminer le ${choix ? 'maximum' : 'minimum'} de $f$ sur son ensemble de définition.<br><br>` +\n mathalea2d(Object.assign({ pixelsParCm: 30, scale: 0.65, style: 'margin: auto' }, { xmin: bornes.xMin - 1, ymin: bornes.yMin - 1, xmax: bornes.xMax + 1, ymax: bornes.yMax + 1 }), objetsEnonce, o) // fixeBordures(objetsEnonce))\n this.question += '<br>'\n this.correction = `Sur l'intervalle $[${theSpline.x[0]}\\\\,;\\\\,${theSpline.x[theSpline.n - 1]}]$, le point le plus ${choix ? 'haut' : 'bas'} de la courbe a pour coordonnées ${choix ? `$(${solsMax[0]}\\\\,;\\\\,${Math.max(...nuage.map(el => el.y))})$` : `$(${solsMin[0]}\\\\,;\\\\,${Math.min(...nuage.map(el => el.y))})$`}.<br>\n On en déduit que le ${choix ? 'maximum' : 'minimum'} de $f$ est ${choix ? `$${miseEnEvidence(`${Math.max(...nuage.map(el => el.y))}`)}$` : `$${miseEnEvidence(`${Math.min(...nuage.map(el => el.y))}`)}$`} . Il est atteint en \n ${choix ? `$x=${solsMax[0]}$` : `$x=${solsMin[0]}$`}.`\n this.canEnonce = 'On donne la représentation graphique d\\'une fonction $f$. <br>' +\n mathalea2d(Object.assign({ pixelsParCm: 30, scale: 0.65, style: 'margin: auto' }, { xmin: bornes.xMin - 1, ymin: bornes.yMin - 1, xmax: bornes.xMax + 1, ymax: bornes.yMax + 1 }), objetsEnonce, o)// fixeBordures(objetsEnonce))\n this.canReponseACompleter = `Le ${choix ? 'maximum' : 'minimum'} de $f$ sur son ensemble de définition est : $\\\\ldots$.<br>`\n }\n}\n"],"names":["dateDePublication","interactifReady","interactifType","titre","uuid","ref","MaxMinG","Exercice","mesFonctions","aleatoiriseCourbe","listeFonctions","coeffX","choice","coeffY","deltaX","randint","deltaY","noeud","bornes","o","texteParPosition","nuage","theSpline","spline","repere1","repere","courbe1","objetsEnonce","solsMax","el","solsMin","choix","mathalea2d","miseEnEvidence"],"mappings":"mSAQY,MAACA,EAAoB,aACpBC,EAAkB,GAClBC,EAAiB,WACjBC,EAAQ,uCAErB;AAAA;AAAA;AAAA;AAAA,EAKY,MAACC,EAAO,QACPC,EAAM,UACJ,SAASC,GAAW,CACjCC,EAAS,KAAK,IAAI,EAClB,KAAK,aAAe,SACpB,KAAK,YAAc,EACnB,KAAK,gBAAkB,EACvB,KAAK,iBAAmB,uCACxB,KAAK,gBAAkB,UAAY,CA+BjC,MAAMC,EAAe,CATL,CAAC,CAAE,EAAG,GAAI,EAAG,GAAI,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EACnF,CAAE,EAAG,GAAI,EAAG,GAAI,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EACpE,CAAE,EAAG,GAAI,EAAG,EAAG,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EACnE,CAAE,EAAG,GAAI,EAAG,EAAG,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EACnE,CAAE,EAAG,EAAG,EAAG,EAAG,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EAClE,CAAE,EAAG,EAAG,EAAG,EAAG,cAAe,GAAI,aAAc,GAAI,UAAW,EAAM,EACpE,CAAE,EAAG,EAAG,EAAG,EAAG,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EAClE,CAAE,EAAG,EAAG,EAAG,EAAG,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,CACnE,EA7Be,CAAC,CAAE,EAAG,GAAI,EAAG,GAAI,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EACnF,CAAE,EAAG,GAAI,EAAG,EAAG,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EACnE,CAAE,EAAG,GAAI,EAAG,EAAG,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EACnE,CAAE,EAAG,GAAI,EAAG,EAAG,cAAe,GAAI,aAAc,GAAI,UAAW,EAAM,EACrE,CAAE,EAAG,EAAG,EAAG,GAAI,cAAe,GAAI,aAAc,GAAI,UAAW,EAAM,EACrE,CAAE,EAAG,EAAG,EAAG,GAAI,cAAe,GAAI,aAAc,GAAI,UAAW,EAAM,EACrE,CAAE,EAAG,EAAG,EAAG,GAAI,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EACnE,CAAE,EAAG,EAAG,EAAG,GAAI,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EACnE,CAAE,EAAG,EAAG,EAAG,GAAI,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,CACpE,EACe,CAAC,CAAE,EAAG,GAAI,EAAG,EAAG,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EAClF,CAAE,EAAG,GAAI,EAAG,EAAG,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EACnE,CAAE,EAAG,GAAI,EAAG,EAAG,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EACnE,CAAE,EAAG,GAAI,EAAG,EAAG,cAAe,GAAI,aAAc,GAAI,UAAW,EAAM,EACrE,CAAE,EAAG,EAAG,EAAG,EAAG,cAAe,GAAI,aAAc,GAAI,UAAW,EAAM,EACpE,CAAE,EAAG,EAAG,EAAG,GAAI,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EACnE,CAAE,EAAG,EAAG,EAAG,EAAG,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EAClE,CAAE,EAAG,EAAG,EAAG,EAAG,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,EAClE,CAAE,EAAG,EAAG,EAAG,EAAG,cAAe,GAAI,aAAc,GAAI,UAAW,EAAM,EACpE,CAAE,EAAG,EAAG,EAAG,GAAI,cAAe,EAAG,aAAc,EAAG,UAAW,EAAM,CACpE,CAU8C,EAC/C,SAASC,EAAmBC,EAAgB,CAC1C,MAAMC,EAASC,EAAO,CAAC,GAAI,CAAC,CAAC,EACvBC,EAASD,EAAO,CAAC,GAAI,CAAC,CAAC,EACvBE,EAASC,EAAQ,GAAI,CAAE,EACvBC,EAASD,EAAQ,GAAI,CAAC,EAE5B,OADcH,EAAOF,CAAc,EACtB,IAAKO,GAAU,OAAO,CACjC,GAAIA,EAAM,EAAIH,GAAUH,EACxB,GAAIM,EAAM,EAAID,GAAUH,EACxB,cAAeI,EAAM,cAAgBN,EAASE,EAC9C,aAAcI,EAAM,aAAeN,EAASE,EAC5C,UAAWI,EAAM,SACzB,CAAO,CAAC,CACH,CACD,IAAIC,EAAS,CAAE,EACf,MAAMC,EAAIC,EAAiB,IAAK,IAAM,IAAM,SAAU,QAAS,CAAC,EAC1DC,EAAQZ,EAAkBD,CAAY,EACtCc,EAAYC,EAAOF,CAAK,EAC9B,KAAK,OAASC,EACdJ,EAASI,EAAU,YAAa,EAChC,MAAME,EAAUC,EAAO,CACrB,KAAMP,EAAO,KAAO,EACpB,KAAMA,EAAO,KAAO,EACpB,KAAMA,EAAO,KAAO,EACpB,KAAMA,EAAO,KAAO,EACpB,QAAS,GACT,QAAS,GACT,iBAAkB,GAClB,0BAA2B,EAC3B,0BAA2B,EAC3B,qBAAsBA,EAAO,KAAO,EACpC,qBAAsBA,EAAO,KAAO,EACpC,qBAAsBA,EAAO,KAAO,EACpC,qBAAsBA,EAAO,KAAO,CAC1C,CAAK,EACKQ,EAAUJ,EAAU,OAAO,CAC/B,OAAQE,EACR,UAAW,IACX,aAAc,GACd,cAAe,CAAE,MAAO,OAAQ,OAAQ,EAAG,MAAO,IAAK,UAAW,CAAG,EACrE,MAAO,MACb,CAAK,EACKG,EAAe,CAACH,EAASE,CAAO,EAChCE,EAAUN,EAAU,MAAM,KAAK,IAAI,GAAGD,EAAM,IAAIQ,GAAMA,EAAG,CAAC,CAAC,CAAC,EAC5DC,EAAUR,EAAU,MAAM,KAAK,IAAI,GAAGD,EAAM,IAAIQ,GAAMA,EAAG,CAAC,CAAC,CAAC,EAC5DE,EAAQnB,EAAO,CAAC,GAAM,EAAK,CAAC,EAClC,KAAK,QAAUmB,EAAQ,KAAK,IAAI,GAAGV,EAAM,IAAIQ,GAAMA,EAAG,CAAC,CAAC,EAAI,KAAK,IAAI,GAAGR,EAAM,IAAIQ,GAAMA,EAAG,CAAC,CAAC,EAC7F,KAAK,SAAW;AAAA,oBACAE,EAAQ,UAAY,SAAS,kDAC1CC,EAAW,OAAO,OAAO,CAAE,YAAa,GAAI,MAAO,IAAM,MAAO,cAAc,EAAI,CAAE,KAAMd,EAAO,KAAO,EAAG,KAAMA,EAAO,KAAO,EAAG,KAAMA,EAAO,KAAO,EAAG,KAAMA,EAAO,KAAO,CAAG,CAAA,EAAGS,EAAcR,CAAC,EACrM,KAAK,UAAY,OACjB,KAAK,WAAa,sBAAsBG,EAAU,EAAE,CAAC,CAAC,UAAUA,EAAU,EAAEA,EAAU,EAAI,CAAC,CAAC,wBAAwBS,EAAQ,OAAS,KAAK,oCAAoCA,EAAQ,KAAKH,EAAQ,CAAC,CAAC,UAAU,KAAK,IAAI,GAAGP,EAAM,IAAIQ,GAAMA,EAAG,CAAC,CAAC,CAAC,KAAO,KAAKC,EAAQ,CAAC,CAAC,UAAU,KAAK,IAAI,GAAGT,EAAM,IAAIQ,GAAMA,EAAG,CAAC,CAAC,CAAC,IAAI;AAAA,0BACjSE,EAAQ,UAAY,SAAS,eAAeA,EAAQ,IAAIE,EAAe,GAAG,KAAK,IAAI,GAAGZ,EAAM,IAAIQ,GAAMA,EAAG,CAAC,CAAC,CAAC,EAAE,CAAC,IAAM,IAAII,EAAe,GAAG,KAAK,IAAI,GAAGZ,EAAM,IAAIQ,GAAMA,EAAG,CAAC,CAAC,CAAC,EAAE,CAAC,GAAG;AAAA,MACvME,EAAQ,MAAMH,EAAQ,CAAC,CAAC,IAAM,MAAME,EAAQ,CAAC,CAAC,GAAG,IACnD,KAAK,UAAY,gEACdE,EAAW,OAAO,OAAO,CAAE,YAAa,GAAI,MAAO,IAAM,MAAO,cAAc,EAAI,CAAE,KAAMd,EAAO,KAAO,EAAG,KAAMA,EAAO,KAAO,EAAG,KAAMA,EAAO,KAAO,EAAG,KAAMA,EAAO,KAAO,CAAG,CAAA,EAAGS,EAAcR,CAAC,EACrM,KAAK,qBAAuB,MAAMY,EAAQ,UAAY,SAAS,6DAChE,CACH"}