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Zuletzt geändert von Stephanie Wietzorek am 2025/05/21 10:29
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Auf Version 12.1
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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 +* Zeichne Tangenten an den Stellen ... ein
14 +* Markiere alle Stellen, wo die Tangente waagerecht ist
15 +* Kann eine Tangente den Funktionsgraphen schneiden?
16 +* Tangentensteigungen bestimmen
17 +
18 +* Bereiche mit positiver/ negativer Steigung schraffieren
19 +* Punktweise graphisch ableiten
20 +* Qualitativ graphisch ableiten
21 +* Zusammenhänge HP, TP, SP vorwärts und rückwärts
22 +
23 +* Funktionsterm der Ableitungsfunktion aus Tangentensteigungen aufstellen
24 +* Zuordnung Polynomfunktionen
25 +* Beobachtungen bei e^x
26 +
27 +{{aufgabe id="Tangenten einzeichnen" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA" zeit="3"}}
28 +Zeichne jeweils die Tangente an den Stellen {{formula}}x\in\{-1, 0, 1\}{{/formula}} ein.
29 +[[image:Tangenten einzeichnen 1.svg|| width="300px"]] [[image:Tangenten einzeichnen 2.svg|| width="300px"]] [[image:Tangenten einzeichnen 3.svg|| width="300px"]] [[image:Tangenten einzeichnen 4.svg|| width="300px"]]
30 +{{/aufgabe}}
31 +
32 +{{seitenreflexion bildungsplan="5" kompetenzen="5" anforderungsbereiche="5" kriterien="5" menge="3"/}}
Tangenten einzeichnen 2.svg
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1 +XWiki.holgerengels
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Tangenten einzeichnen 4.svg
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