import{r as X}from"./reperes-uV74d7Az.js";import{h as m,n as Y,o as C,aa as T,a as l,s as h,l as w,r as G}from"./index-XCg2QAX4.js";import{s as j}from"./Spline-RTcaFHGe.js";import{E as Q}from"./Exercice-FKaS4mj7.js";import"./courbes-lqVoJQXx.js";import"./etudeFonction-dMwwHtDn.js";import"./MatriceCarree-rFs_Ninq.js";import"./Polynome-CQLyV74s.js";const W="Graphically determine the extrema",K=!0,U="mathLive",Z="27/06/2023",_="7761e",ee="2F32-2",E=[{x:-4,y:-1,deriveeGauche:0,deriveeDroit:0,isVisible:!0},{x:-3,y:1,deriveeGauche:2,deriveeDroit:2,isVisible:!1},{x:-2,y:4,deriveeGauche:0,deriveeDroit:0,isVisible:!1},{x:-1,y:1,deriveeGauche:-2,deriveeDroit:-2,isVisible:!1},{x:0,y:-3,deriveeGauche:0,deriveeDroit:0,isVisible:!1},{x:2,y:2,deriveeGauche:0,deriveeDroit:0,isVisible:!1},{x:3,y:-2,deriveeGauche:0,deriveeDroit:0,isVisible:!1},{x:4,y:1,deriveeGauche:0,deriveeDroit:0,isVisible:!0}],I=[{x:-5,y:3,deriveeGauche:0,deriveeDroit:0,isVisible:!0},{x:-3,y:4,deriveeGauche:0,deriveeDroit:0,isVisible:!1},{x:-1,y:-3,deriveeGauche:0,deriveeDroit:0,isVisible:!1},{x:2,y:2,deriveeGauche:-.5,deriveeDroit:-.5,isVisible:!0}],O=[{x:-5,y:0,deriveeGauche:-2,deriveeDroit:-2,isVisible:!0},{x:-4,y:-3,deriveeGauche:0,deriveeDroit:0,isVisible:!1},{x:-2,y:1,deriveeGauche:0,deriveeDroit:0,isVisible:!1},{x:0,y:0,deriveeGauche:-.5,deriveeDroit:-.5,isVisible:!0}],P=[{x:-5,y:0,deriveeGauche:-2,deriveeDroit:-2,isVisible:!0},{x:-4,y:-3,deriveeGauche:0,deriveeDroit:0,isVisible:!1},{x:-2,y:1,deriveeGauche:0,deriveeDroit:0,isVisible:!1},{x:0,y:0,deriveeGauche:-.5,deriveeDroit:-.5,isVisible:!0}],B=[E,I,O,P];function F(r){const i=Math.floor(Math.min(...r.map(s=>s.x))-1),a=Math.floor(Math.min(...r.map(s=>s.y))-1),o=Math.ceil(Math.max(...r.map(s=>s.x))+1),d=Math.ceil(Math.max(...r.map(s=>s.y))+1);return{xMin:i,xMax:o,yMin:a,yMax:d}}function L(){const r=m([-1,1]),i=m([-1,1]),a=G(-2,2),o=G(-2,2);return{coeffX:r,coeffY:i,deltaX:a,deltaY:o}}class ie extends Q{constructor(){super(),this.titre=W,this.sup="4",this.nbQuestions=1}nouvelleVersion(){this.listeQuestions=[],this.listeCorrections=[],this.autoCorrection=[];for(let i=0;i<this.nbQuestions;i++){const{coeffX:a,coeffY:o,deltaX:d,deltaY:s}=L(),t=m(B).map(e=>Object({x:(e.x+d)*a,y:(e.y+s)*o,deriveeGauche:e.deriveeGauche*a*o,deriveeDroit:e.deriveeDroit*a*o,isVisible:e.isVisible})),c=j(t),{xMin:f,xMax:v,yMin:p,yMax:b}=F(t),V=Y("O",-.3,-.3,"medium","black",1),y=X({xMin:f-1,xMax:v+1,yMin:p-1,yMax:b+1,grilleX:!1,grilleY:!1,grilleSecondaire:!0,grilleSecondaireYDistance:1,grilleSecondaireXDistance:1,grilleSecondaireYMin:p-1,grilleSecondaireYMax:b+1,grilleSecondaireXMin:f-1,grilleSecondaireXMax:v+1}),g=c.courbe({repere:y,epaisseur:1.5,ajouteNoeuds:!0,optionsNoeuds:{color:"blue",taille:1,style:".",epaisseur:2},color:"blue"}),M=[y,g];let n=`We give the representative curve of a function $f$ defined on the interval $[${c.x[0]}\\,,\\,${c.x[c.n-1]}]$. <br>`;n+="Determine the extrema of the function and specify at what values they are reached.<br>",n+=C(Object.assign({scale:.7},T(M)),M,V),this.interactif&&(n+="<br>The maximum of $f$ is:"+l(this,4*i,"inline width10 nospacebefore"),n+=". It is reached at $x=$"+l(this,4*i+1,"inline width10 nospacebefore"),n+="<br>The minimum of $f$ is:"+l(this,4*i+2,"inline width10 nospacebefore"),n+=". It is reached at $x=$"+l(this,4*i+3,"inline width10 nospacebefore"));const $=c.solve(Math.max(...t.map(e=>e.y))),D=c.solve(Math.min(...t.map(e=>e.y))),u=$.length===1?$[0]:"We have a problem",x=D.length===1?D[0]:"We have a problem";h(this,4*i,Math.max(...t.map(e=>e.y))),h(this,4*i+1,u),h(this,4*i+2,Math.min(...t.map(e=>e.y))),h(this,4*i+3,x);const S=`The highest point of the curve has coordinates $(${u}\\,,\\,${Math.max(...t.map(e=>e.y))})$.<br>We deduce that the maximum of $f$ is $${Math.max(...t.map(e=>e.y))}$. It is reached at $x=${u}$.<br>The lowest point of the curve has coordinates $(${x}\\,,\\,${Math.min(...t.map(e=>e.y))})$.<br>We deduce that the minimum of $f $ is $${Math.min(...t.map(e=>e.y))}$. It is reached at $x=${x}$. `;this.listeQuestions.push(n),this.listeCorrections.push(S)}w(this)}}export{Z as dateDePublication,ie as default,K as interactifReady,U as interactifType,ee as ref,W as titre,_ as uuid};
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