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(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 10.3' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 221021, 4799] NotebookOptionsPosition[ 207455, 4590] NotebookOutlinePosition[ 207885, 4607] CellTagsIndexPosition[ 207842, 4604] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Laboratorio No. 4\nC\[AAcute]lculo I - MAT1610", FontFamily->"Arial", FontSize->36, FontColor->RGBColor[0.5, 0, 0.5]], StyleBox["\nSemana 6 - 10 Mayo 2019\n", FontFamily->"Arial", FontSize->24, FontColor->RGBColor[0.5, 0, 0.5]], StyleBox["\n", FontSize->24], StyleBox["Mar\[IAcute]a", FontSize->18], StyleBox[" ", FontSize->18, FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["Trinidad", FontSize->18], StyleBox[" ", FontSize->18, 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"Introducci\[OAcute]n", StyleBox["\n", FontColor->RGBColor[1, 0, 0]], StyleBox["Recordemos que el signo de la derivada en un intervalo determina \ si ella es creciente ( derivada positiva) o \ndecreciente ( derivada negativa \ ) en dicho intervalo. \n\nUna funci\[OAcute]n continua creciente o \ decreciente en un intervalo alcanza su m\[AAcute]ximo o m\[IAcute]nimo en un \ extremo del intervalo. \n\nUn punto cr\[IAcute]tico b es un punto donde la \ derivada de la funci\[OAcute]n se anula, f \[CloseCurlyQuote](b) = 0. \n\nSi \ en la vecindad del punto cr\[IAcute]tico b la derivada cambia de signo, el \ punto f(b) es un m\[AAcute]ximo local o un m\[IAcute]nimo local. \n", FontSize->18, FontColor->RGBColor[0, 0, 1]], StyleBox["\n ", FontSize->18], "\n", StyleBox["Comandos para calcular m\[AAcute]ximos y m\[IAcute]nimos", FontSize->36, FontWeight->"Bold"], "\n\[AliasDelimiter]\n", StyleBox["El comando", FontSize->24], StyleBox[" ", FontSize->24, FontColor->RGBColor[1, 0, 0]], 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Se entiende por \[AAcute]rea de la caja la \ suma de las \[AAcute]reas de sus 6 caras.\n\n1.1 Encuentre una \ funci\[OAcute]n A(x) que represente el \[AAcute]rea de la caja con tapas. \ LISTO\n Precise el dominio de la funci\[OAcute]n para el problema y gr\ \[AAcute]fique A en su dominio. Explique. LISTO\n1.2 Observando el gr\ \[AAcute]fico de A encuentre el valor aproximado del \[AAcute]rea \ m\[IAcute]nima. LISTO\n1.3 Calcule y gr\[AAcute]fique la derivada de la \ funci\[OAcute]n A. LISTO\n1.4 Encuentre todos los valores donde la \ derivada de A se anula. LISTO\n1.5 A partir del gr\[AAcute]fica de la \ derivada de la funci\[OAcute]n examine si existe un punto p donde A tiene un \ m\[IAcute]nimo local. \n Explique su respuesta. LISTO\n1.6 \ \[DownQuestion]Es A(p) un m\[IAcute]nimo absoluto? Explique su respuesta. \ LISTO\n1.7 Explicite las dimensiones de la caja con tapas de volumen 4 \ metros c\[UAcute]bicos de m\[IAcute]nima \[AAcute]rea. 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