(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 92459, 2239] NotebookOptionsPosition[ 87916, 2083] NotebookOutlinePosition[ 88318, 2100] CellTagsIndexPosition[ 88275, 2097] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Substitu\[CHacek]n\[IAcute] pravidla a voliteln\[EAcute] argumenty\ \>", "Title", CellChangeTimes->{{3.57200121396875*^9, 3.572001230078125*^9}, { 3.5782055954410515`*^9, 3.5782056123785515`*^9}, {3.5782057113004265`*^9, 3.5782057143316765`*^9}}], Cell[CellGroupData[{ Cell["Substituce hodnot do funkce", "Subsection", CellChangeTimes->{{3.5782056271910515`*^9, 3.5782056347379265`*^9}}], Cell[TextData[{ "Aplikujte pravidla a mechanismus substituce k v\[YAcute]po\[CHacek]tu lok\ \[AAcute]ln\[IAcute]ho maxima a minima funkce f(x). Nejd\[RHacek]\[IAcute]ve \ nalezn\[EHacek]te v\[SHacek]echna \[RHacek]e\[SHacek]en\[IAcute] z rovnice f\ \[CloseCurlyQuote](x) = 0, potom ur\[CHacek]ete znam\[EAcute]nko funkce f\ \[CloseCurlyQuote]\[CloseCurlyQuote](x) v bodech z a nakonec \ vyhodno\[THacek]te hodnotu funkce f(z) v bod\[EHacek] z. P\[RHacek]ed zah\ \[AAcute]jen\[IAcute]m v\[YAcute]po\[CHacek]t\[URing] funkci v\[ZHacek]dy \ nakreslete. \na) Ur\[CHacek]ete v\[SHacek]echny extr\[EAcute]my polynomi\ \[AAcute]ln\[IAcute] funkce f(x) = 0.4 ", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["x", "3"], " "}], TraditionalForm]], FormatType->"TraditionalForm"], "- 7.1 ", Cell[BoxData[ FormBox[ SuperscriptBox["x", "2"], TraditionalForm]], FormatType->"TraditionalForm"], " + 10.0 x - 3.5\nb) Ur\[CHacek]ete mimimun funkce f(x) = x + 10 sin(x) v \ prvn\[IAcute]m kvadrantu\nc) Uva\[ZHacek]ujte n\[AAcute]sleduj\[IAcute]c\ \[IAcute] polynom p(x) stupn\[EHacek] 13: \np(x) = x-", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{"2", SuperscriptBox["x", "3"]}], "3"], TraditionalForm]], FormatType->"TraditionalForm"], "+", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{"3", SuperscriptBox["x", "5"]}], "10"], TraditionalForm]]], "-", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{"53", SuperscriptBox["x", "7"]}], "315"], TraditionalForm]]], "+", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{"1489", SuperscriptBox["x", "9"]}], "22680"], TraditionalForm]]], "-", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{"4541", SuperscriptBox["x", "11"]}], "207900"], TraditionalForm]]], "+", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{"100319", SuperscriptBox["x", "13"]}], "13899600"], TraditionalForm]]], " \nUveden\[YAcute] polynom je dobrou aproximac\[IAcute] fukce sin(x cos(x)) \ na intervalu [-1,1]. Ur\[CHacek]ete lok\[AAcute]ln\[IAcute] minimum a maximum \ polynomu na intervalu [-1,1]. 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