"Nalezněte extrémy funkce f(x) na intervalu [-10 , 10]" x = 2 a x = 3 nepatří do definičního oboru x f(x) -10 0.634615385 -9.9 0.631945802 max: 78.27272727 -9.8 0.629237288 min: -82.33333333 -9.7 0.626488997 -9.6 0.623700055 -9.5 0.620869565 -9.4 0.617996604 -9.3 0.615080222 -9.2 0.612119438 -9.1 0.609113245 -9 0.606060606 -8.9 0.60296045 -8.8 0.599811676 -8.7 0.596613148 -8.6 0.593363696 -8.5 0.590062112 -8.4 0.586707152 -8.3 0.583297534 -8.2 0.579831933 -8.1 0.576308982 -8 0.572727273 -7.9 0.569085349 -7.8 0.565381708 -7.7 0.561614799 -7.6 0.557783019 -7.5 0.553884712 -7.4 0.549918167 -7.3 0.545881616 -7.2 0.541773231 -7.1 0.537591122 -7 0.533333333 -6.9 0.528997844 -6.8 0.52458256 -6.7 0.520085318 -6.6 0.515503876 -6.5 0.510835913 -6.4 0.506079027 -6.3 0.501230729 -6.2 0.496288441 -6.1 0.491249491 -6 0.486111111 -5.9 0.480870431 -5.8 0.475524476 -5.7 0.47007016 -5.6 0.464504284 -5.5 0.458823529 -5.4 0.453024453 -5.3 0.447103482 -5.2 0.441056911 -5.1 0.43488089 -5 0.428571429 -4.9 0.422124381 -4.8 0.415535445 -4.7 0.408800155 -4.6 0.401913876 -4.5 0.394871795 -4.4 0.387668919 -4.3 0.380300065 -4.2 0.372759857 -4.1 0.365042715 -4 0.357142857 -3.9 0.349054286 -3.8 0.340770791 -3.7 0.332285939 -3.6 0.323593074 -3.5 0.314685315 -3.4 0.305555556 -3.3 0.296196466 -3.2 0.286600496 -3.1 0.276759884 -3 0.266666667 -2.9 0.256312695 -2.8 0.245689655 -2.7 0.2347891 -2.6 0.223602484 -2.5 0.212121212 -2.4 0.2003367 -2.3 0.188240456 -2.2 0.175824176 -2.1 0.163079866 -2 0.15 -1.9 0.136577708 -1.8 0.122807018 -1.7 0.108683151 -1.6 0.094202899 -1.5 0.079365079 -1.4 0.064171123 -1.3 0.048625793 -1.2 0.032738095 -1.1 0.016522423 -1 3.10862E-15 -0.9 -0.016799293 -0.8 -0.033834586 -0.7 -0.051051051 -0.6 -0.068376068 -0.5 -0.085714286 -0.4 -0.102941176 -0.3 -0.119894598 -0.2 -0.136363636 -0.1 -0.152073733 0 -0.166666667 0.1 -0.179673321 0.2 -0.19047619 0.3 -0.198257081 0.4 -0.201923077 0.5 -0.2 0.6 -0.19047619 0.7 -0.170568562 0.8 -0.136363636 0.9 -0.082251082 1 -1.11022E-16 1.1 0.122807018 1.2 0.305555556 1.3 0.579831933 1.4 1 1.5 1.666666667 1.6 2.785714286 1.7 4.846153846 1.8 9.333333333 1.9 23.72727273 2 2.1 -37.88888889 2.2 -24 2.3 -20.42857143 2.4 -19.83333333 2.5 -21 2.6 -24 2.7 -29.95238095 2.8 -42.75 2.9 -82.33333333 3 3.1 78.27272727 3.2 38.5 3.3 25.35897436 3.4 18.85714286 3.5 15 3.6 12.45833333 3.7 10.66386555 3.8 9.333333333 3.9 8.30994152 4 7.5 4.1 6.844155844 4.2 6.303030303 4.3 5.849498328 4.4 5.464285714 4.5 5.133333333 4.6 4.846153846 4.7 4.594771242 4.8 4.373015873 4.9 4.176043557 5 4 5.1 3.841781874 5.2 3.698863636 5.3 3.56916996 5.4 3.450980392 5.5 3.342857143 5.6 3.243589744 5.7 3.152152152 5.8 3.067669173 5.9 2.98938992 6 2.916666667 6.1 2.848937844 6.2 2.785714286 6.3 2.726568006 6.4 2.671122995 6.5 2.619047619 6.6 2.570048309 6.7 2.52386429 6.8 2.480263158 6.9 2.439037153 7 2.4 7.1 2.362984218 7.2 2.327838828 7.3 2.29442738 7.4 2.262626263 7.5 2.232323232 7.6 2.203416149 7.7 2.17581187 7.8 2.149425287 7.9 2.124178485 8 2.1 8.1 2.076824172 8.2 2.054590571 8.3 2.033243486 8.4 2.012731481 8.5 1.993006993 8.6 1.974025974 8.7 1.955747578 8.8 1.938133874 8.9 1.921149595 9 1.904761905 9.1 1.888940199 9.2 1.873655914 9.3 1.858882366 9.4 1.844594595 9.5 1.830769231 9.6 1.81738437 9.7 1.804419461 9.8 1.791855204 9.9 1.779673454 10 1.767857143 ##### Sheet/List 2 ##### "Najděte maximum funkce y = x^2-5 na intervalu [0,5] pomocí Řešitele" Max: 20 Příprava pro řešitele: 5 20 ##### Sheet/List 3 ##### Operace s maticemi x1 x2 x3 1 2 3 -1.791666667 0.916666667 -0.125 A= 4 5 6 A-1 = 1.583333333 -0.833333333 0.25 7 8 1 -0.125 0.25 -0.125 5 -5.541666667 x1 b= 4 x = A-1b = 5.083333333 x2 2 0.125 x3 Zkouška: 5 Ax= 4 2 AT = 1 4 7 (A-1)-1 = 1 2 3 2 5 8 4 5 6 3 6 1 7 8 1 A*A-1 = 1 1.11022E-16 0 A-1*A = 1 0 0 -3.33067E-16 1 0 2.22045E-16 1 0 -5.55112E-17 0 1 0 -1.11022E-16 1 ##### Sheet/List 4 ##### Operace s maticemi 2 x1 x2 x3 x4 5 8 1 2 -0.85046729 -0.878504673 0.831775701 0.504672897 A= 2 5 4 3 A-1 = 0.728971963 0.46728972 -0.570093458 -0.289719626 6 8 1 4 -0.429906542 -0.224299065 0.23364486 0.299065421 4 9 7 2 -0.074766355 0.439252336 0.08411215 -0.252336449 1 -0.542056075 x1 b= 8 x = A-1b = -0.392523364 x2 7 0.308411215 x3 3 3.271028037 x4 Zkouška: 1 Ax= 8 7 3 AT = 5 2 6 4 (A-1)-1 = 5 8 1 2 8 5 8 9 2 5 4 3 1 4 1 7 6 8 1 4 2 3 4 2 4 9 7 2 A*A-1 = 1 -4.44089E-16 2.22045E-16 3.33067E-16 A-1*A = 1 -1.77636E-15 0 -6.66134E-16 -5.55112E-16 1 2.77556E-16 2.22045E-16 2.22045E-16 1 0 1.11022E-16 -4.44089E-16 -2.22045E-16 1 2.22045E-16 0 4.44089E-16 1 0 -5.27356E-16 -7.77156E-16 4.71845E-16 1 0 0 2.22045E-16 1 ##### Sheet/List 5 ##### "Najděte graficky maximum funkce 2x+3y za podmínek x,y >= 0, x+y<=10 a x>=y" Cílová funkce: 2x+3y Podmínky: x+y<=10 x>=y x>0 y>0 Maximum: x=5 y=5 Cílová funkce: 25 ##### Sheet/List 6 ##### "Najděte graficky maximum funkce x+2y za podmínek x,y >= 0, x+y<=100 a 2x<=y" Cílová funkce: x+2y Podmínky: x+y<=100 2x<=y x>0 y>0 Maximum: x=0 y=100 Cílová funkce: 200 ##### Sheet/List 7 ##### Řešte pomocí Řešitele: x1 x2 x3 x4 f(x) 1.232977848 2.4659466 6.926346051 16.38193935 1224.995683 Podmínky: L P 169.0000003 169 ##### Sheet/List 8 ##### Řešte pomocí Řešitele: Najděte maximum funkce x*y*z za podmínek nezápornosti a x+y+z<=12 x y z cílová f 4 4 4 64 podmínky L P 12 12