Eine Brotbäckerei hat monatliche Fixkosten von 3500€. Bei einer Warenmenge von 4,5 ME betragen die Kosten 5000€. Die Kosten steigen am wenigsten bei einer Warenmenge von 7,5 ME. Sie steigen dann um genau 50€/ME. Bestimmen Sie die Kostenfunktion.
Bedingungen: [br][list=1][*][math]K(0)=3500[/math][/*][*][math]K(4,5)=5000[/math][/*][*][math]K''(7,5)=0[/math][/*][*][math]K'(7,5)=50[/math][/*][/list]Das sind vier Bedingungen, daher kann man daraus eine ganzrationale Funktion 3-ten Grades erstellen. Eine ertragsgesetzliche Kostenfunktion ist sehr oft eine Funktion dritten Grades:[br][math]K(x)=a_3\cdot x^3+a_2\cdot x^2+a_1\cdot x+a_0[/math] Wir benötigen hier auch die Prototypen von [math]K'(x)[/math] und [math]K''(x)[/math]:[br][math]K'(x)=3\cdot a_3\cdot x^2+2\cdot a_2\cdot x+a_1[/math][br][math]K''(x)=6\cdot a_3\cdot x+2\cdot a_2[/math][br][br]Setzt man die vier Bedingungen in die Prototypen ein, dann erhält man das Gleichungssystem:[br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAa4AAABGCAYAAACUlXDBAAAqqUlEQVR4nO3dB7QkRbkHcNFrxoABEZ8BJCmogCiIIrpgWHISJAhKDgJLWKLgEyQuyAKSVyQjSBZdA6KIIklABV1QQcWAGDCDkcdvfd9a2/SkO93TM3frf86ce6e7Z6a6q+rLYezRRx99QkZG4JOf/OQHnv3sZ//xZz/72f/86le/etHhhx9+QNNjyijH73//++decMEFmz35yU/+xze/+c03bb755uevttpqX256XBkZdWOs6QFkDA/+/e9/P/G4447b49vf/vbr5ptvvkcXXHDBB6dMmTLd36bHlvF4fPzjH//gm970pm9iVmuttdbVyy677B0PPPDAQuau6bFlZNSJuRjX9773vVf/6U9/etaKK654U1MDyqgff/7zn+e/8sor18WoFl100Xvf/OY3f8PxJz7xif/+zne+81r/33jjjSu9/vWv/1ZmWs3jhz/84WI0KvO1+uqrX/OSl7zk5477/znPec4f/P/MZz7zL4888sjTXPOkJz3pX82OePTwhz/84Tmf/exn1/znP/859qpXver7b3jDG25pekyjhJ///Ocv+fznP//uv//9709ZaqmlZr397W//Spz7xje+8eY//vGPz37d6173bfzl1ltvXWG99da7wpp1/i9/+csz0aNHH310vpe97GU/XWWVVa5Pv/u2225b/vvf//6rzM0666xz1QILLPDQbMZ1xRVXrHfPPfcsceaZZ269++67H58Z18TF3/72t6e+973v/ZS5xpRoWHffffeSW2+99ZlxzbXXXjvp4osv3nj77bc/vd13MSc+hp/VP+p5FzbtCSecsJv5snG33HLLc5hvCRwrrbTSjXHdscceu9cRRxyxfzumdf/997/0Mdw/mJGPDhDOTTfd9MKzzz57qxe+8IW/PvTQQw/60Y9+9Er7pOx6JvTnPe95v2OiHfRYhxE/+MEPFr/kkks22m+//Y7817/+9aQ111zzs1/96lff9pGPfOTDzl9//fWr7L///kf4/wUveMFvPvaxj+0ZTOsf//jHk9/znvd8+rTTTtvB2pw+ffqUu+66a+kdd9zxVOc/85nPrP21r33trdOmTZvKNL7ZZptdcP75528+m3Hhfv66oJE7/3/gqgsvvPAvQorMqB7nnnvu+xZffPEfhCa10047nfLKV77yR1tttdXZQfQmTZp0rdcKK6xwqw266qqrXlf2XR/60Ic+etZZZ71/gMOf53DQQQcdOnXq1Gm04ac85Sl/R0wPOeSQg9Pn/qlPfeq9L3/5y3+SCh9lwNhOPvnknWsf9Ijh9NNP395ax7S8J7wvs8wyd26yySYXlZldL7vssg3e8pa3fP01r3nNdwc/2uHDl7/85dU++tGPfmjfffc9amxs7J+0rZNOOmmXYFzw29/+9vkPPfTQAq94xSt+nApXmNBiiy32wxCodt5555MJZdtss80nCAb77LPP0ddcc83qzj33uc/9PbP4iSeeuOtQ+bie9axn/cnN4shNj6UTSBbUYxoHotL0eLoFc8hb3/rWr8X7pz3taY884xnP+CtT1MMPP/z0T3ziE9sghM696EUv+hVpqhXjIi0Natz9glTNTLHQQgs90PRYuoX5+MpXvvL2U045Zac4tsgii9w3c+bMycwqiOpVV121jnt629ve9lVS7wYbbHBZU+uRRviLX/xiYURolPxsTFyeW7wXnMQycccddyy73HLL3d7EmH73u989zzNkFmvi93sBKwDzXqy7e++9d1FmwfQaArBX8bPWcvqMCWe0MeZFZsNZs2YtFaZxwNSOPvrofYaKcWECnM0zZszY9jHMaHo8rSB4ATGhtl599dVrWfgISNPj6gZMIO9617u+kB57+tOf/jBT8dprr/0ZkifNl5MfIWJCaWqsVcFcYVqvfe1rv8N3xw9Ea2l6XJ3AFIt5mZ84hpA9+OCDC/LJkHR32GGH08JCgTBstNFGlzQx1ptvvvmNTG20FHuBuZlm0sRYegVTOaE5PUag41scNOOy55jV/C7N5KabblqR68ZzHeQ4egHBd+mll77L/2jjnXfeuYxo1/QaDMpaJtigMWHm9uwJXcXvQ48ID4SI9Byty7mBMi7BH8cff/zuna4zeT/5yU9efsABBxyebtphwE9/+tOXIeY0FAQDATEZ6TV8CdTiJZdc8u6nPvWpf0vPhaQ82FH/F8ZbXAyAsDOV7Lnnnh8ToMGUiCGPkuRcBuH9mBWi6j1tcokllrgnzmNipDpSHnNb+lnnmtSmaYn+kkKL5zi7J0+ePJNGHMeYaQY5voAxEDTtCc/RfrD+i9cRhso03qb3hGcZPpfA/PPP/2d7ZdBj4dtZfvnlbyMUe/+/j0HEaJxHG9FRJreyfRwgSLCedPq9jTfe+OKqUijOOeecLTEuwV4YTBxndmVWpZiw0oh+vfTSSzcUxIHuYFTp98SzNy/FNc186NxAGderX/3q73HCdXMtYrLuuuteufLKK99g8moeWtcgDYlsCSmXIzGd+GOOOWZvE2ODvuMd7/gSySMCGNzHl770pXdQg5saf3GRBILBItTGXzxP+qQJp8eYUjhk02MkqfCZNg2bgt2dgzeO0SbD8fvXv/71GaeeeuqONtoXvvCFd33rW996PQYXNniSodyovfba69gmxl/GsAJh4m01n6K0MJL0GAZenC8Mh4+hn3HywXGwB/H/7ne/+5o0quyGG25Y2TH+jKIf3WedIyT1M4Z+4BkWzd4ibwnNtITUVwO33377ciLjwicGzFr8M/2Mw/q76KKLNhGM473f/uUvf/liVijvEWzPa4899jiONmsNtAogeeMb33izVz/j6RVMhv7yd9GibrnlljdgNCnj9R6NoMCwhHj2omHT77FvPXsvLpn0HC3M8YEyLtKCQXW6zo1wIpMoBQ0MYmzdwEO8/PLL1083meiZ3Xbb7YR4b3EJfiC9kzosxmBcCHqo1E2BOUl0TnrM8+7k+0HcMIH0GLNj8VhRcm0S5obWFBuYBMc0gSF5z+l73333LULLZI4R/m++4noMq2irHyREYPmLgIWg5B4IGZ0CmOyd1JcJv/71r19YnK9UMh4PMH/m8g9/+MMfiWOe+5FHHrlfvCd8WvfnnXfeFsXPb7jhhpdGOkZT8JxDuw0gkPYEIsnykxJQEZ6IL0E8jmEi/Y4DbeErCmGE4EGIDKsTjcZ54fpe/icwlEWSYsSYb6ff9FtFq1CvsGdoSSxM3lt3gor4Z+0pa45fKnxcfg/t8D/mX2RcQY+cMw/pOfyD770rxmXSqsgNMVimm3bXcEqSDNnJqcP9/maVkKOAiFB9vfdQaU9CxxFBeTVCaR23eS04BCQ+bxGWaTODBCJBiov3CDsTTpHIlaHoKKYRDLPz2MZFMMMMZU7k51jL5otGHIzJcyB0PP/5z/9tfJ621dTYgblWxKcgoBAs/I8RdCI25qaosflM1fMVxJHZx1+MlSbuOfPBdTJDpSH9TcHztAfivf2LQMbYiiY5xN6xqp+l30wFJWsUc+LrdI75L0yIQBEw7jR4IUCLRZc6/abQ9WLeVK+gaQnICYE+GBH6J3WA68FY43o0Ppg+bTKlR8zGfLjoEWbIVMjsHM+aGVqw2JwvQ5RJHaSydFA+JJLpwgsv3DQlwuMBjpxKYkUYNHXbgk/V8GGBiSCZ26weJJXeXwuZ7yuuY1YzYQiPa8uiaZqC5/u+973v3BBGmC6ZZIdpjFXBphA663/zweaPkRE2pF2Yz/Brmctdd931RIyi2VHPDdKqPEuSq/ek8lTDbxrWOKZF88Io5eF4poSFlCANM8y7l9Br4xZ5ixgP2nqAWF933XWr+p85EiNgGsTAtthii/PQ4tQ0jF5iAmWMi5/MaxDjpjWn5sAvfvGL77T3vLgeBAwFPceEMeAwGQsuYu4MeiSoR/BYpOt88IMf/Lj1/4EPfOCT3tPumW7H4oc8MHZJKiZfDOJmEzMlsFmGeaVOYFjrr7/+5cPItAKkGD4TEhczJpMNPxaV3XmhoIijFyfqwQcffIjSPE2PO0CLpbbzxVnwFlK3fsdRg3v1/JlYbHg5bO7VZpeHE9eZU5oWDQsBbuU3agLbbbfdGY9hO5YKkqxxD4sPMYCwEGxF5mEATG98NbEnhh3MbnISpeEwQ2G4GPCgxyEkn6CLntCwP/3pT7+Hr5LpmubhWOpqYSEYBoGTmVhe4de//vW30Kz4sTDdCKzAdOR1sWqwGBCWw33CN+hZe/aESYFtqS9d9C/6aQ+7X0IbbX4243rnO9/5Ra+yQZFAcL1BPACmtkH8Tj/woHfZZZeT4n1aXYJE5DnSuLyvysRaNUIa6vd7mFiqGE+dePe73/359D0JNn3Pyc0kIZiApG1DNZW70wqYVxXfU1fCLP9nSiPKghRoB3X8dlUgtBfDslvBGqmDYaC1RZ8+/2v8TyP78Y9//Ar/YxCUijJta9BA4yQMtzpPEWnHQ9oFkmCCglGKx4cqj2vUwWyoHI/oKUyL2bWdaXTUkTLwUYQIw6OOOmrf1PGuPE2TY6oTqqQ08btMQ/J4SOAkb6alUUoEL0K+YxO/Kw2HdiOlAwOzdpsYxzAgM66KIS8i/o/w0IzhBBORBM+mxzHRERJ1GnmY0TtoH7nN0H+QGVdGRkZGxkghM66MjIyMjJFCZlwZcyFqiok2FB2W5o1kDBeksPCnigRWdkmgkOT3pseVkVE3MuPKmAPhqiJ4BC2IcMK45FSkSbkZwwMlcySUS1WReiGXRmWQpseVkVE35jAu+Ucy3oV6ipMf9eKq8xok5qVJgO0gAZeznLNXXoiCxqqBSBZUtcTcS6iWV9FvSaCMx0M+lnI+aT2/VpA4/Zvf/OYFUSpMNJlEX3OjWkFUrpBzqXyVMOmmiu0OG6Q3qAzRzbUSYgkBQrvlC1n/ud9W9+j0/FTDkOdFGFapI+UvUiXsB/lzUmxe/OIX/zL9bnmXvl+eoD2DTs1mXJIHbQabQx0uGeQmfZjqzmW0hkmX+Nkt47KZlbWxECRQq9Qc5zAqCYKKz6oX2S4PjamqXSHYjHJI8FcaqRvGpZireY2yQz4TLSPSHlLqAMqVace05iWmZg2rMdgt41JGSL1BOX2Iqwolra5lms3dj+dGu+eH6ciXlBrEmqPhqSo2GBCmpXqGJGVpBvaG74rWSzqAS8BXMAEzFKmNR43pTKliBSKFCKmqoG+Rv8WqyHUjt8TuHRiQKgXMfN1+xuQjgEyA6rEVmY8afs5LxEUkW0meCKXusf3ew7wEG1EIvlD8bj+jYj0hUsm0qJOZQvV1dUCPPfbYvdp9z5QpU6YPUxWXukALVXWil6RnOW7WvWRZe6Idg0d0JQOnRXbndbR7fvI9dV/A2NAUwjJlSaUaVYgIAlEQQfcC1/DZYmxojKox1r89w4er+s3sjqUmwpeEBKjQo5L0g7556qRBFlsvZLQG57zExHYSYhHMTEprFY8zE/oeiY0WnhqV1PtWjKtYUTujPWxQGpSN3UuvJxu51RyYM5Va5Peo80ZabaUl9yLcjDIk6Kp/59l0+xkVccr2RBkwxGK7jXkdrZ6fpo/KOKE5cYzwpZQVnuNvVJUHlgUMK9xW5jA9zypIWB6zISx8LZHTH2uiarOxqJuoine35VeaAAZLdfUQEXiVmJuokKFpm6aIvdbW42PBoJiO2Jqja67Clr7LpqT9WnDDVhdvPLCeVMRQu9D9YrjME4MeBymTkNFrEim/lqALdRRZQ6LDABOx+1Dk1nzyV06aNOnaWgbfAWrQ6bGEKNkTuuA2kSxLm/V8iq0yOsGzveSSSzay9hVf1nOvrjF2Ao0iOl+zPmEKw14Or9Xzw4CK3aXRGEWE43yxGLDPO88aWKRtXBnOzfZxpRWxcTgbpY622+ybnYpXkmYwL+HYKiJXPYZ+oZeV+nf8QjQSf7VgKTKuuv0Jvt9cIVwYZy+fVVORPdn4pk2bNlXvHO1YCC9UfvfknH46ox6cwddx3HHH7cEkQRMh5RXb5QzC9yPqjwRZ3MSdQAK1FzA8ewMBU3iUI9z3pW2C+BeqH3lnKG3GDydASO08pk0VzYuMq+7anczmWmio7chS0MtnBQDwGZL2VfhAq4q9ywYBLhr784gjjtjfe3Ugrd/0mm6eI82eb6jT722yySYXVSHsFJ+f9c5yVtbh2B4Ii0M0jUzPR2d554puDObGx3VAJokKh8Y46ijeyEbZbSVyzIAvBpMYplwizkOtTTAt75laU+2Q5EvaI9lTg4UsB/G3kPgjOvUk6wZhDhnPZ0nG8b+6cSR2/g8+L1pXWrYqoO8PwpSam2jqRR8XM7PnM55xVQ3BI+zr/Dqx0d1HtEhwL+bExuF7subTIryeL8mx3/WH0Oi+MJ5agWmvJGtqjTXW+Bzfsz0qqtCr7HM0Dxp5egwxSecLkRG8UIzi6hUHHnjgYfpuBc0QHZYGnmAiNDDCg6Cv9LPWIm2Sj72fMQCz+Xh7qKW+P3uCzyWCXfh50w7J7sc6SjtMEyLMTT/jpzDoxCE61HvrBkOINWAM5p6Ggu7426rQtRSJQXT0CJQ9PwFjNMair5F2FoKiv0Wza5z3Kpq3Q8icw7h8mITB39W009FgOZsR0mHrj6R8P5NPvKeVkIbjPW2FBsMuK2hC4IuJdE5h0WB4/cCzIRFGoVILHbMk5WJC0TKgDPwgCFYwW8/YhkDU2jWUI83TyNKFFMfS67SF6Pf+qgLzIAITRNQz0q01Ou7SxhAAxEAbH4IV4hOh56TdKlrsEFQ8Z/PjPQJFSPTePLTT9jAazCWYAmmUeaXTbxZbYADtLZ0v66BXDbAIwoGIRs73OGZPEITivVYs3AAYS/Hz7qvY5XY8wBhppgTDeC9IwzNmvmxX1FcLDs8mmABBE/G0z3wWDXKfcf1dd921tD2W7uUq1j0Gqe9a5E2KMzBfIfg673dpNqF9oy/9/m6/aPX8BFjE/+n1nmVU11eYvDj/9qnjXmkDSrCmfXbOQf1QSJvRWE9PlMcwo8obRBxJFMXBFG+KBKaKdFk5+yaB2FBT0665Qj1pVRaZ/LdoT44gMqGktmnmuSoqSws3TUOhbSREyER36oxLw7DJgnExffob894KmFTRpIAgD7PtneSPCUWUKgnZexoWU4p5DDMFbQYDSSVra7WKcWh1kzZotf6jG3G7fEnri7nF3ATjEkbfaa7ANcXrmP+rni9mLf6Y2BP2r+csqo+QEA0wWyH8q/2C8z8NfbdXadmecaeUDdqe8QfhDYaPSdhXxe7gCLIYgKrzvKzXtAMy36zf9oy9CGIRAGHdGCfBrIwpW9/Mjp1+c8cddzy1X1Nhq+fHGoDJ8FVhtLHW+c+jHx5/pJiB9PviPCENU0t75MW52QyEPZVzlfnJe4svfoTUYuOxs/ZrAqLJRQ5KK+y///5H8LcMY/KfkExSeDAHhNv/GAEzCMbluDYOTCLMnHU0JTShKUGw4BHd9JgFyQRUrMht4afmhc997nNrOMYBXPU4m4ZAhiBa1jRzhgg9AhQLgw0fm55ZlyYWgQ9VwrNNny9iiqjGfEUfN/7f0AYB0WSaDmZj85Nuh60DMgIfWiMi5pnS5PibOjGuqoBApj2yZs2atZS9mf4+1wMCu9deex2bfpafJ+1HaC/TwAfdpNF6xRT9jyERglnBzLkgKccinw8IZJLTyxgXM6EGqYMYN9dC5F2B5yc+geboJUyeMBN0h9k8Isf56FPtnKZMuAxtljWLBh9CCWauZ9kYswXzkYNpuZj4MhsfEyHl1/0ASBTU8mFkWgFddGktFovqE/wgtNNoWIi4RBsHG+Swww47EPGpazxMlxglmzKmb8MREJgqiz4OIOHyMyKKCCbNsAqf2zACIWCmRQBoBQQ0idWeV9qwTyURAS7O1Tke0qP1EKYRQgUzJYczgipaKmVcoIswPxABSLSv+TPHdY6zFxBw7QkMC5HCANAULoemIvOsZz4+BFASsiaH6Io94RkWr7eH7Wl7gvTPr8SKMuhxv//97z+L0M4VgY54pkyBhC2WAQIrjTuuZ/0pBjY0AcwlfX7oSrqXrAXWCwnEzLnWRaxze1QwjfMipJl6U+XmxBNP3NU+ca+YNOVg8uTJM8dEWLH1txoUxjWo1u6IfTs/yzCAiSBNFUiTPpndMF1h5N5j9iFB1QWL3at4nJk1rYgRsLgECYTDtJ/SXq0CA4YJRe2ESTx9j4mxNmjdzm/ILFGXlkADEBFYPI74EH7K5ovWrAtuFRF5ddWcLHYPbqLtfQrBNxGAk0IQSVm+o+fKQsE0az902hOEiDosKTSo4vpIzZToTmpWc33Rx9wEOj0/fmLCV6uKIxEj4HwxMAyztp6Knx2qIrud/DPDDo5IfkJSEp8Q/1dTlQpIje02YBW1KEe9uzPfYGjKNh6nMLNrE2MR3BCm5jJUEUZOmu/3O8YDwgFzF4nZfqA1NtEBmamtXVUeQl0335Nq64MEAXXvvfc+hjmblYAZcZhqynZ6fp0qIrU7Xzw3VIxrIoCEb4NQ6YWP15m30g5C1dddd90rm/jtUQFTEgbf9DiAT2gi+hkhTOcHH3zwIU2OQzHpbmsXDiOsESZMVhwpGoP2wQ0TMuOqAanTvykgFE3+fkZvaJWPk1EdhiW/sB/QatISSPMqMuPKyMjIyBgpZMaVkZGRkTFSyIwrIyMjI2OkMIdxSdBUOkgI90Ru1S6jXri6qgLDkANRByTYjqdsl/wiYadRrFV4qyCTpgrtSi+QE2Kuuo34ysjImFiQuiMgRWh8lNaazbhkJou40aRLZWeJYrpMTrTutpLZRJGpRCApVeJbN+VzRg2KW6ocTwhJ6+BpOyCZsdXnJGcK6lC8UzQkJq90z6AZF4Yp74MAJa9KvT6h92l1g4yMjIkPvEjSPlotQV8x7Nn9Ap2UrOolm1kFBqWNlPAYdIZ+nS2xJVHL6I+EYSVJaCUTkXG5JxMdofgYkJIr7ZhWQOKmhEGVBlRtaKeVRuWHKscOKjFIRI/q1ur0Gcu999676ES2BmRkZMyN3Xff/XgVgaLavZxApQlnMy6tAFQV938UwG0i/0i7ACVBqmaYEktVRkh79ChCqWZclb8zDFDaSCa6+mBxTKkjfbe6+bw8l25zXeSKjXec7YDJ0rBUsvBe9QAmS8f1farjNzMyMoYL9ryar2lvSEn6um7MZlJpDyLFRjGxaMUxSGg/ITOc1qeYbVXfi2HROiTwqe3HBIoAjtdvwhekAoACo8xxzI/j7QNUNWhIKdOSBK2aclqcsx34OhXJ9FduUb+9msaDffbZ5+hUeIkyN573eL5PewqLn7amdYm6Z1ExIyMjYzjBLMjVkVYHoWxwg8wJziDdat6oWjjCVUf5JYVMO5VAoh2p+MDXVlUjNI49AQdajyibojQ+wuVee/XfMGcqEqlwLgarICZVdlgYVwoMVikhvr1uP6PIpXppFgvhRfHLbkyMVUL9tbQGm6KpGhWOJ6namtMQ0FwzgSs3pMZiZlwZExmIezfFs+3xYfUdC84quirsYcfnMC6SqJebIKGrLRbmw6qgAG03BXuZK4855pi92TK1IlBBuJ/fpT3ohxQFfEWmKC7sN8p6LinE6t7LOpqecMIJu5HcMS3vMdq026sFw5eGaWCYytxEkItixiq20yr7uZ9uYeGm/X06QdM8PXxCwmEyVOFe9wAmSNGK6fU0TT2X0mM0NL2RqrmD/5h0PTcdf8vO06RpaAqoFn9XNNL2229/uiK1Frxj1kJaEFbwCQ3MXJlT7SOqGntGRlMoFgMfRdi/xe7IArccf1weF+lafx0FHJkNBzfM/4J6KLKN1sUZ1y/jol4ylaW1vWhavrvsetErrbrSYmoi3uK9/jAp46KJOa8sCyJI0g9iyCdE6+vnXnoBs2havb4TMAmRpaGFCorgV7JYNIMrMqkyxkX4qYpxETZoi5hWK3+kfnGEBeMr/q75NZchgNgEipNaV977n09VYBJN2tit/4kYsJORMWoQ/h5dLAKaVKLlYyqYM82paI5ZOIlwieCqeiCqcdNYOl0nn0ynYCHrVVQ/dl80oLQ1hAfSykwoqq3sOCKpf1Xa9gLjEl3HjyIS74orrlhPfyW/J5QzNXdqJ+LV7/10A+o0JtlLIU4alnvZZZddTvJeKLpFwhdImKG9pNdrCFc8VhVoQZiWoqJaSKgsjvEXpUjac5F5BoT3Y0ahbWl5r5AtJhgRihGlKJrVs9LiJDOujFGHfmRSmjpdJ1p3WLuYi/rGqFhJwmpFmBWgMSZggQkvWoOTrvm7oi+KDwlJZN5CmPsZiGrcnUyFGBsCWmUTOiYwv60ja/hr3OPOO+98ci/fw08mVDyI3cyZMydjZvwxtBvPB9PyOxaNBnYIflX30Qvcn7kMoh1wDGMSLh+CSoDmEUwLaCRN+O6sOWPZYIMNLuNzc4y5stdoU+bgNHxecztCBy0L47JhwxyO+dkLo25eycgABYVHvaiwQuV824I0Yl/6H10YQ8j5kURd4XDRwjxaviMiJFUSb7+MqxMQWyGQdXROZR5ixqPx0ET48YpNy7oBxuqFKIoo9KxoaCkTYNrU/GzbbbedgVjq9VTt3XQGnxRtFTFOj5tPAQs0wyLj0sKcadFxZjZMWRfWwY78CU846aSTdqHNecUxmnKvOWN8mhiTjqrMmuuvv/7l559//ubWejonku91aRWUlCt0ZGQMDxQfwIsoBCxxrGZyTWf7uBBYRIq5S75Tal6iZfBzDGKQzFIc7XV8N61LsMfdd9+9JObFfjqe79Hm28ND4DAG0WmCSfjEMF0mziC4/EVC8ZtgXPxu7rXoG7IAjKnMf0lzpOkwsVkTnZJ96yqZFQnxVXyXKNY0sV3wUeq/xLRUFGGW1ETS5qCdV/HbGRkZ/WGRRRa5T5AZNxO3C+HT8TnBGRhULxFodSDMlXUBwaqCKBWTs4MQeoZMUbRTDIJ5KzTXQQNTxTjLzvEV0RbLzmHI3UaTduOvHAbM1fI7YVoYFbO0SEhRtHyS119//SrNjDIjI6MM6G0xQC9Xh68QiL5wcrUfabBMiONNmq0TpJcquiMLmqhiPE1BrmJEGAaGcb4yMjLmRmZcFYNEn1auGEZUwbQmApjE5+X25xkZo4rMuDIyMjIyRgqZcWXMBYm8kqaFzdPMmurFlZGRkdEKmXFlzIGoyHPOOWdLuVwCOFRlF2DSKpAjIyMjowmUMi4ErNtq4hnNQEa55OIq846EwV9zzTWrC0WX0ydvT2UVCX9V/UbG45H3W0ZGb3gc41IXTnJqE4mndUJCrYoWwsTVtpOJrbJF0+MaLyTpSqZV6VwYfhxXwsWr3WcxJWVT5GnJW8KYVKWQJ6H/jWvkqs2aNWupplIkJA0zW6pyYRx6ihl3E2OpE8pqaeGjNJWqLCGIiNhUjaXdZ6VaqCwiR1GJLN9FY55oncszJjasfbRHRC96xEWx1VZbne0cAV0HZOHw0ozkjqr6MxfjEsJtMwy6jUXdUJeQ+Qux1xpj8uTJM+WMyeka1RI/anYpHiuROvLK5CIx73X6rGK05lo4uHJeabX0gHWgRXa7aikzZszYVqJyXzdSAj42ydCbbbbZBd6fccYZ27nXO++8c5mUSU8ESBL3/G3eSC+weZdYYol7On2WEKb24v333/9SFVxs6HZMS3WQURbWMiYm0GJdHjCpXXfd9cS0aLlSg4qUo9nea0tF0JuLcZHgEQiJmYMePCj0iwiXEdJ+gHHFw/E+zDIPPPDAQlX+ziBBuNhiiy3Oi/dMeqQSRWc7fVaNvv322+/IVudVm1ARBDGUlIs4ll0nX60OxqX0khYqUYFEzyDFfGnKw1oQdLzApNS1DIZM01WarJvKIZLcMaNuf0s9xsy4MoYNreiRQuV4UtrDcdKkSdfKvZzDuJR1oo1oPDioAReB0yJQiPJ4SzKVgfmF+TPek+hx7X6aCerjpBcX8xVmu+yyy95RxVi7Rcq0mIkUxNXQstvPq3KPaGJ2aT1D/cnkohFe1C1UqLMV46oLCvsKDon3TGD+jtefx4ek3BdCb40RYKruNTdeFP2HTPRKhHXbFcEa1OONmTFtvjkM0Ectqu0bn2feql1QxrwN9EgfQwXfgx4pqJuWawOBYjpyzGZcFj8JlzRWJ+PSrE+B03bXCL9WT47UXXUVA8WCMS3+LtI8Qtbrd9De1DpEAPmF1NEiLeiqXOVYe4GGmJoldnu9+1dkmBlQd2Dqt/uhXTE7uQZT87cOjaoTjM0r3l966aUbInrRCLQXYMDmib+I1q3WmXWleGe1o+4faoVKQ+i29Jl9e9FFF22igjZt9PDDDz+AWbWKVkD9gpnZvRCmdFEwn9ZUq75qGdWCP99z73Qd10I0xW0KUfQcPWIqtF+t6fBppdeyljk+m3FRx8KfUCdUVO8UOACI5aGHHnoQu7/K9VX5NWhF/FqkWprdhRdeuGmxejpcffXVa9EyyhpY+gzJQCV170X2pURW0VYOc5uW2cf445yq7DZvldXvBS+IBuyFICDaEeKOcWln7zvcczcdqgcJz9N8CRpJJa+AAsd8bdZvWWQeH565ivYyhJVVV131ujivNqF7J/HRftJalhimwAdNQeu6vxS6ZXNEd3u9uYt5NIdqR9IsN9100wvrG2VnRNt43R68p23Z+7FGzRkBSSBJU7U8Jzr4SLuhm924FuoGmhPrmIlc/VAWF6bCYl1YcHyMOoZB1FXpOwXC0605Y8qUKdN32GGH05gaetnM3Yxht912O4GWwixGMixeQ3Ll35k2bdrU4jmfmTp16rR4T21ld433CKUuye6TQ1EB1ygBdfHFF28sarNKxkWT6KVwMLNb2qOLlEPTQmTamTtpy55ZeozmZo7SYySl8bSLaTVW3QJUsmfaLbuGRkXbJGSsvPLKN6Tn1GSk4acRsjRt8+N/VgbXMM1pe6JAMukvNtFBBx10KJPsAQcccHgV99MOfp+PlxDZ7WeKmhXmQMrGuJiypTak53UFKM4X53erYszjhf3KLxnjK3YJJ4wQFIwxM656QEAbNtNxGYr0yBpG82mM3EWE//R6Zn/HxzTUY6KIqtgkWxIRgs4kVmV+CUJByup0HRMIf8bll1++fplG1CsELtggpFEShg0lsq5V51zXl9niPWQEPo1EtCk9J4RH3TvPTYg6k+KDDz64IMYV19IiSdX93k8KhKoXbZk5mDbIxOS9//0ttsguAnEramN8UXVpaBas/luYDNOZiCMMtsikPWs+vjJtjFBm3MGIzJ31ZO6F2vvOMPGaO3NljUZkps0zKJ+MRO9e1jqfNOGK5hKmRc8snkNZWoTGqYNIc8H801Y+9oiIx9gjhCWv3PusPtx6660raNfT6Tp+/qqD4XoByxe6Gi6koENotJYmGFW0jXJcZ3dxBWNMDOkXkYb83XfffY+KL7LYSdFU/n4GyU8R39sKgigeeuihBXrx2XSC6EGEKt67J/e59dZbn1l2fStiRYohHURrd6a/IKYqwcs9YFa6/fbbl+NrsFmZmtLvKCOw/cBvlXVy5iNkmknNmMD5mTI6xN0CcbzKcfULDEvDOCHiQv8JVK3SNFo9U+s1DSyh8cpfs75oH/JFokuseRS04XxcP8hAAvNQZu61dmkm5jg1m2DYGDsmHMesR1rioMbcCgQF4/M/4Q3jYs61JiM/J6Ne2CvdNP5tOr1EnijtPN6jZ+Gmka7jL1N+5HASLJkS50QV6oyrW68NjbAff/zxu9MkbGamkjB99TNIElY7X4xNavOFKacqyAOQA0TixnxOOeWUnTDRAw888LBevsf4OZv5Pkjn/FXMrDS0lEBaNEI4+Uz4VtZaa62rq7yfAFuvTsdlQSb8HeaOvy09TsLh4xKQgYCLHGSeGqZoL2NnIkybinr2cs96+R5htnL3BOWIvCN0eFa0TdpiXEfzopEL3BmEybwMJMvUZBIgOQv+YcZNg1OsK2vO2iM4WdMk5258yHUDvbjqqqvWIUmzahgfv3DZ/WXUA0LOKATCsACFj9o+ZLFSfADTct665qKwj1kXWEHs3zmMi9QqmiMkIiYkx9w8Fb/MSVY1SNa9MpNuICnzkEMOOfimm25akb8EAaD5jSf6yvg4DhFAhJHGigFg7JgI/xemhdDSdkxCXYzL5DKnisIsnpOMnKYABEjD/HBysMwxLWS8qQd1rQmL2VpMj5mrXpkKZswEQWAxTwgnYcP9hlnOZiEoeRHYSHfdJP9WDT5d+6x43NqhDRK8iufsVRtZJHAxsKRJIEKChpj8Jf6zbGBco5rsn1EfmI5FEjKVMwly56SFvUU8sgjR1u1f5k/0fA7jQhhacehBMC2o21zFLBSmoX6QBgp4ZvHcMCvEJ+y0cqvqjtakTZYdNxYaWdk5C6AKZspU1e93lMH4qpLOCV9pdKhNEP/TckQcIvgCcjC4pkqdtQo+AeuolR/CvZVFv5ahSvN7J0QUJxA4WCbiPeuOfcJ8zxFPmAoJO2Peg/XB/Nfq/EILLfRAMeArV4evEDYf05uQeY5yJp4qGOV4QOOq2+maMoFRBG0r9XNKwB90snUnMI/SXKoIkmrHHAcJLgHWj+nTp09hyl5++eVv68Yfk5ER+D+1oj4y1UlRRAAAAABJRU5ErkJggg==[/img][br]Lösen mit dem CAS (HP Prime):[br][list=1][*]a3*x³+a2*x²+a1*x+a0 als k(x) abspeichern (im Prime müssen für Funktionen leider kleine Buchstaben als Name verwendet werden)[/*][*]Damit: solve({k(0)=3500,k(4.5)=5000,k' '(7,5)=0,k'(7.5)=50},{a3,a2,a1,a0})[/*][*]Das führt zu [math]a_3\approx3,23[/math], [math]a_2\approx-72,6[/math], [math]a_1\approx595[/math] und [math]a_0=3500[/math][/*][/list]Also heißt die gesuchte Kostenfunktion: [math]K(x)=3,23\cdot x^3-72,6\cdot x^2+595\cdot x+3500[/math][br]