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, // fltk 8Fl_Group 833 105 89 299 20 0 [ // fltk N4xcas14Mouse_PositionE 833 105 89 40 20 0 [] , // fltk 8Fl_Group 833 145 89 115 20 0 [ // fltk 9Fl_Button 833 145 29 23 20 0 [] , // fltk 9Fl_Button 862 145 30 23 20 0 [] , // fltk 9Fl_Button 892 145 29 23 20 0 [] , // fltk 9Fl_Button 833 168 29 23 20 0 [] , // fltk 9Fl_Button 862 168 30 23 20 0 [] , // fltk 9Fl_Button 892 168 29 23 20 0 [] , // fltk 9Fl_Button 833 191 29 23 20 0 [] , // fltk 9Fl_Button 862 191 30 23 20 0 [] , // fltk 9Fl_Button 892 191 29 23 20 0 [] , // fltk 9Fl_Button 833 214 29 23 20 0 [] , // fltk 9Fl_Button 862 214 30 23 20 0 [] , // fltk 9Fl_Button 892 214 29 23 20 0 [] , // fltk 9Fl_Button 833 237 29 23 20 0 [] , // fltk 11Fl_Menu_Bar 862 237 59 23 20 0 [] ] , // fltk 8Fl_Group 833 260 89 144 20 0 [ ] ] ] ] , // fltk 7Fl_Tile 23 406 899 31 20 0 [ // fltk N4xcas23Comment_Multiline_InputE 23 406 899 30 20 0 a vue de nez la courbe coupe y=0 en x=1.6 environ, plus précisément , // fltk N4xcas10Log_OutputE 23 436 899 1 20 0 ] , // fltk 7Fl_Tile 23 439 899 54 20 0 [ // fltk N4xcas19Multiline_Input_tabE 23 439 899 30 20 0 fsolve(-x^2+2x-1+2*exp(-x),x=1.6) , // fltk N4xcas10Log_OutputE 23 469 899 1 20 0 , // fltk N4xcas8EquationE 23 470 899 23 20 0 1.62694383142 ] , // fltk 7Fl_Tile 23 495 899 108 20 0 [ // fltk N4xcas19Multiline_Input_tabE 23 495 899 30 20 0 f(x):=(x^2-2x+1)*exp(x) , // fltk N4xcas10Log_OutputE 23 525 899 45 20 0 // Parsing f£// Success compiling f£ , // fltk N4xcas8EquationE 23 570 899 33 20 0 (x)->(x^2-2*x+1)*exp(x) ] , // fltk 7Fl_Tile 23 605 899 330 20 0 [ // fltk N4xcas19Multiline_Input_tabE 23 605 899 30 20 0 graphe(f(x),x=-5..5) , // fltk N4xcas10Log_OutputE 23 635 899 1 20 0 , // fltk 7Fl_Tile 23 636 899 299 20 0 [ // fltk N4xcas7Graph2dE 23 636 810 299 20 0 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, // fltk 8Fl_Group 833 636 89 299 20 0 [ // fltk N4xcas14Mouse_PositionE 833 636 89 40 20 0 [] , // fltk 8Fl_Group 833 676 89 115 20 0 [ // fltk 9Fl_Button 833 676 29 23 20 0 [] , // fltk 9Fl_Button 862 676 30 23 20 0 [] , // fltk 9Fl_Button 892 676 29 23 20 0 [] , // fltk 9Fl_Button 833 699 29 23 20 0 [] , // fltk 9Fl_Button 862 699 30 23 20 0 [] , // fltk 9Fl_Button 892 699 29 23 20 0 [] , // fltk 9Fl_Button 833 722 29 23 20 0 [] , // fltk 9Fl_Button 862 722 30 23 20 0 [] , // fltk 9Fl_Button 892 722 29 23 20 0 [] , // fltk 9Fl_Button 833 745 29 23 20 0 [] , // fltk 9Fl_Button 862 745 30 23 20 0 [] , // fltk 9Fl_Button 892 745 29 23 20 0 [] , // fltk 9Fl_Button 833 768 29 23 20 0 [] , // fltk 11Fl_Menu_Bar 862 768 59 23 20 0 [] ] , // fltk 8Fl_Group 833 791 89 144 20 0 [ ] ] ] ] , // fltk 7Fl_Tile 23 937 899 31 20 0 [ // fltk N4xcas23Comment_Multiline_InputE 23 937 899 30 20 0 On conjecture 3 solutions pour m entre 0 et 1.4 environ, 1 au-dela, 0 en-deca , // fltk N4xcas10Log_OutputE 23 967 899 1 20 0 ] , // fltk 7Fl_Tile 23 970 899 54 20 0 [ // fltk N4xcas19Multiline_Input_tabE 23 970 899 30 20 0 factor(deriver(f(x)) , // fltk N4xcas10Log_OutputE 23 1000 899 1 20 0 , // fltk N4xcas8EquationE 23 1001 899 23 20 0 (x+1)*(x-1)*exp(x) ] , // fltk 7Fl_Tile 23 1026 899 31 20 0 [ // fltk N4xcas23Comment_Multiline_InputE 23 1026 899 30 20 0 donc f croit si x<-1 et x>1 et décroit entre -1 et 1 , // fltk N4xcas10Log_OutputE 23 1056 899 1 20 0 ] , // fltk 7Fl_Tile 23 1059 899 54 20 0 [ // fltk N4xcas19Multiline_Input_tabE 23 1059 899 30 20 0 limit(f(x),x=-infinity),f(-1),f(1),limit(f(x),x=+infinity) , // fltk N4xcas10Log_OutputE 23 1089 899 1 20 0 , // fltk N4xcas8EquationE 23 1090 899 23 20 0 0,4*exp(-1),0,+(infinity) ] , // fltk 7Fl_Tile 23 1115 899 52 20 0 [ // fltk N4xcas23Comment_Multiline_InputE 23 1115 899 51 20 0 On dresse le tableau de variations de f, on prouve qu'il y a 0 solutions si m<0,£1 solution si m=0 (x=1), 3 solutions si m>0 et mf(1) , // fltk N4xcas10Log_OutputE 23 1166 899 1 20 0 ] , // fltk 7Fl_Tile 23 1169 899 31 20 0 [ // fltk N4xcas19Multiline_Input_tabE 23 1169 899 30 20 0 , // fltk N4xcas10Log_OutputE 23 1199 899 1 20 0 ]