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Zuletzt geändert von Stephanie Wietzorek am 2025/05/21 10:29
Von Version 1.1
bearbeitet von holger
am 2022/11/13 18:11
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Auf Version 16.1
bearbeitet von Holger Engels
am 2025/05/20 12:56
Änderungskommentar: Neues Bild Tangenten einzeichnen 1.svg hochladen

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Titel
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1 -Graphisches Ableiten
1 +BPE 6.3 Momentane Änderungsrate und graphisches Ableiten
Übergeordnete Seite
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1 -Main.WebHome
1 +Eingangsklasse.WebHome
Dokument-Autor
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1 -XWiki.holger
1 +XWiki.holgerengels
Inhalt
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1 -{{box cssClass="floatinginfobox" title="**Contents**"}}
2 -{{toc start=2 depth=2 /}}
3 -{{/box}}
1 +{{seiteninhalt/}}
4 4  
5 -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.
3 +=== Kompetenzen ===
4 +[[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann Werte der Tangentensteigung graphisch bestimmen
5 +[[Kompetenzen.K4]] [[Kompetenzen.K1]] Ich kann aus Werten der Tangentensteigung einen Graphen zeichnen und diesen als Graphen der Ableitungsfunktion deuten
6 +[[Kompetenzen.K6]] Ich kann Zusammenhänge zwischen den beiden Funktionsgraphen beschreiben
7 +[[Kompetenzen.K4]] [[Kompetenzen.K1]] Ich kann erste Hypothesen über einen möglichen algebraischen Zusammenhang zwischen Funktion und Ableitungsfunktion entwickeln
8 +
9 +{{lernende}}
10 +**Interaktiv Erkunden:** [[Graphisches Ableiten>>https://kmap.eu/app/browser/Mathematik/Differentialrechnung/Graphisches%20Ableiten#erkunden]]
11 +{{/lernende}}
12 +
13 +* Kann eine Tangente den Funktionsgraphen schneiden?
14 +
15 +* Bereiche mit positiver/ negativer Steigung schraffieren
16 +* Punktweise graphisch ableiten
17 +* Qualitativ graphisch ableiten
18 +* Zusammenhänge HP, TP, SP vorwärts und rückwärts
19 +
20 +* Funktionsterm der Ableitungsfunktion aus Tangentensteigungen aufstellen
21 +* Zuordnung Polynomfunktionen
22 +* Beobachtungen bei e^x
23 +
24 +{{aufgabe id="Tangenten einzeichnen" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA" zeit="3"}}
25 +Zeichne jeweils die Tangenten an den Stellen {{formula}}x\in\{-1, 0, 1\}{{/formula}} ein und bestimme deren Steigungen.
26 +[[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"]]
27 +{{/aufgabe}}
28 +
29 +{{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
Tangenten einzeichnen 1.svg
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Tangenten einzeichnen 2.svg
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Tangenten einzeichnen 4.svg
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