Änderungen von Dokument BPE 6.3 Momentane Änderungsrate und graphisches Ableiten

Zuletzt geändert von Stephanie Wietzorek am 2025/05/21 10:29

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Von Version 21.1

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Seiteneigenschaften

Titel

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--BPE 6.3 Momentane Änderungsrate und graphisches Ableiten
++Graphisches Ableiten

Übergeordnete Seite

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--Eingangsklasse.WebHome
++Main.WebHome

Dokument-Autor

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--XWiki.wies
++XWiki.holger

Inhalt

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--{{seiteninhalt/}}
++{{box cssClass="floatinginfobox" title="**Contents**"}}
++{{toc start=2 depth=2 /}}
++{{/box}}
--=== Kompetenzen ===
--[[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann Werte der Tangentensteigung graphisch bestimmen
--[[Kompetenzen.K4]] [[Kompetenzen.K1]] Ich kann aus Werten der Tangentensteigung einen Graphen zeichnen und diesen als Graphen der Ableitungsfunktion deuten
--[[Kompetenzen.K6]] Ich kann Zusammenhänge zwischen den beiden Funktionsgraphen beschreiben
--[[Kompetenzen.K4]] [[Kompetenzen.K1]] Ich kann erste Hypothesen über einen möglichen algebraischen Zusammenhang zwischen Funktion und Ableitungsfunktion entwickeln
--
--{{lernende}}
--**Interaktiv Erkunden:** [[Graphisches Ableiten>>https://kmap.eu/app/browser/Mathematik/Differentialrechnung/Graphisches%20Ableiten#erkunden]]
--{{/lernende}}
--
--* Kann eine Tangente den Funktionsgraphen schneiden?
--
--* Bereiche mit positiver/ negativer Steigung schraffieren
--* Punktweise graphisch ableiten
--* Qualitativ graphisch ableiten
--* Zusammenhänge HP, TP, SP vorwärts und rückwärts
--
--* Funktionsterm der Ableitungsfunktion aus Tangentensteigungen aufstellen
--* Zuordnung Polynomfunktionen
--* Beobachtungen bei e^x
--
--{{aufgabe id="Tangenten einzeichnen" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA" zeit="3"}}
--Zeichne jeweils die Tangenten an den Stellen {{formula}}x\in\{-1, 0, 1\}{{/formula}} ein und bestimme deren Steigungen.
--[[image:Tangenten einzeichnen 1.svg|| width="350px"]] [[image:Tangenten einzeichnen 2.svg|| width="350px"]] [[image:Tangenten einzeichnen 3.svg|| width="350px"]] [[image:Tangenten einzeichnen 4.svg|| width="350px"]]
--{{/aufgabe}}
--
--{{aufgabe id="Rauf und runter" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA" zeit="3"}}
--Markiere jeweils auf der x-Achse Intervalle mit positiver Steigung blau und negativer Steigung rot. Markiere die Stellen mit Steigung Null.
--[[image:Tangenten einzeichnen 1.svg|| width="350px"]] [[image:Tangenten einzeichnen 2.svg|| width="350px"]] [[image:Tangenten einzeichnen 3.svg|| width="350px"]] [[image:Tangenten einzeichnen 4.svg|| width="350px"]]
--{{/aufgabe}}
--
--{{aufgabe id="Punkte mit gegebener Steigung finden" afb="?" kompetenzen="" quelle="Stephanie wietzorek und SImone Kanzler" cc="BY-SA" zeit="3"}}
--Es ist das Schaubild K_f einer Funktion f gegeben. Kennzeichne Punkte auf K_f, für die gilt:
--  f'(x) =1
--  f'(x) = 1,5
--  f'(x) = -17/4
--  f'(x) = 0
--Tipp: Zeichne dir ein Steigungsdreieck und verschiebe es
--[[image:Tangenten einzeichnen 1.svg|| width="350px"]] [[image:Tangenten einzeichnen 2.svg|| width="350px"]] [[image:Tangenten einzeichnen 3.svg|| width="350px"]] [[image:Tangenten einzeichnen 4.svg|| width="350px"]]
--{{/aufgabe}}
--{{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
++Die Schülerinnen und Schüler bestimmen grafisch Werte der Tangentensteigung, zeichnen davon ausgehend den Graphen und deuten diesen als Graphen der Ableitungsfunktion. Sie beschreiben Zusammenhänge zwischen den beiden Funktionsgraphen und entwickeln erste Hypothesen über einen möglichen algebraischen Zusammenhang.

Arbeitsheft 6.3. Graphisches Differenzieren.ggb

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Arbeitsheft 6.3. Graphisches Differenzieren.svg

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Tangenten einzeichnen 2.svg

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1		-XWiki.holgerengels

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Tangenten einzeichnen 3.svg

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Tangenten einzeichnen 4.svg

Author

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1		-XWiki.holgerengels

Größe

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Inhalt

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Tangenten einzeichnen.ggb

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Änderungen von Dokument BPE 6.3 Momentane Änderungsrate und graphisches Ableiten

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