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Änderungen von Dokument BPE 6.3 Graphisches Ableiten

Zuletzt geändert von Holger Engels am 2025/08/02 07:35
Von Version 60.1
bearbeitet von Holger Engels
am 2025/05/20 14:03
Änderungskommentar: Neues Bild Aussagen.svg hochladen
Auf Version 59.1
bearbeitet von Stephanie Wietzorek
am 2025/05/20 13:54
Änderungskommentar: Es gibt keinen Kommentar für diese Version

Zusammenfassung

Details

Seiteneigenschaften
Dokument-Autor
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1 -XWiki.holgerengels
1 +XWiki.wies
Inhalt
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1 1  {{seiteninhalt/}}
2 2  
3 +=== Kompetenzen ===
3 3  [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann Werte der Tangentensteigung graphisch bestimmen
4 4  [[Kompetenzen.K4]] [[Kompetenzen.K1]] Ich kann aus Werten der Tangentensteigung einen Graphen zeichnen und diesen als Graphen der Ableitungsfunktion deuten
5 5  [[Kompetenzen.K6]] Ich kann Zusammenhänge zwischen den beiden Funktionsgraphen beschreiben
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9 9  **Interaktiv Erkunden:** [[Graphisches Ableiten>>https://kmap.eu/app/browser/Mathematik/Differentialrechnung/Graphisches%20Ableiten#erkunden]]
10 10  {{/lernende}}
11 11  
13 +* Kann eine Tangente den Funktionsgraphen schneiden?
14 +
15 +* Bereiche mit positiver/ negativer Steigung schraffieren
12 12  * Punktweise graphisch ableiten
13 13  * Qualitativ graphisch ableiten
14 14  * Zusammenhänge HP, TP, SP vorwärts und rückwärts
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43 43  | [[image:Polynome zuordnen i.svg||width=200]] | | | | | [[image:Polynome zuordnen D.svg||width=200]]
44 44  {{/aufgabe}}
45 45  
46 -{{aufgabe id="Skizzieren anhand Eigenschaften" afb="?" kompetenzen="" quelle="Stephanie Wietzorek, Simone Kanzler" cc="BY-SA" zeit="4"}}
50 +{{aufgabe id="Skizzieren anhand Eigenschaften" afb="?" kompetenzen="" quelle=" Stephanie Wietzorek, Simone Kanzler" cc="BY-SA" zeit="4" interaktiv="Interaktiv Zuordnung"}}
47 47  Es ist ein zur y-Achse symmetrisches Schaubild einer Funktion 4. Grades gesucht. Folgende Angaben sind bekannt, fülle die Lücken.
48 48  (% class="border" %)
49 -|{{formula}}x{{/formula}}|-4|-1|0|1 |4
50 -|Funktionswert|-2,5| |2 |0|
51 -|Tangentensteigung|-2| |0|-1 |
53 +|= {{formula}}x{{/formula}} |-4|-1|0|1 |4
54 +| Funktionswert an der Stelle x |-2,5| |2 |0|
55 +| Tangentensteigung an der Stelle x |-2| |0|-1 |
52 52  {{/aufgabe}}
53 53  
54 54  {{aufgabe id="Aussagen Polynomfunktion I" afb="I" kompetenzen="" quelle="KMap" cc="BY-SA" zeit="3"}}
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62 62  
63 63  {{aufgabe id="Aussagen Polynomfunktion II" afb="?" kompetenzen="" quelle="Stephanie Wietzorek, Simone Kanzler" cc="BY-SA" zeit="?"}}
64 64  Eine weitere Funktion hat folgendes Schaubild. Nimm Stellung zu folgenden Aussagen und begründe deine Antwort.
65 -[[image:Aussagen.svg|| width="700px"]]
69 + [[image:Aussagen.svg|| width="700px"]]
66 66  ☐ {{formula}}f(-3)=3{{/formula}}
67 67  ☐ {{formula}}x = 3{{/formula}} ist dreifache Nullstell
68 68  ☐ die Tangentensteigungen sind negativ für {{formula}}x \in ]2;5[{{/formula}}
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70 70  ☐ an der Stelle {{formula}}x = 2{{/formula}} liegt eine waagrechte Tangente
71 71  ☐ die Tangentensteigungen sind negativ für {{formula}}-4 < x < 2{{/formula}}
72 72  ☐ die Tangentensteigungen haben einen Vorzeichenwechsel bei {{formula}}x=-4{{/formula}} von ⊝ ⇾ ⊕
77 +
73 73  {{/aufgabe}}
74 74  
80 +
81 +
75 75  {{aufgabe id="Aussagen Sattelstelle" afb="I" kompetenzen="" quelle="KMap" cc="BY-SA" zeit="3"}}
76 76  Welche Aussagen treffen auf eine Sattelstelle zu?
77 77  ☐ Eine Sattelstelle hat eine waagrechte Asymptote
Aussagen.svg
Author
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1 -XWiki.holgerengels
1 +XWiki.wies
Größe
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1 -20.5 KB
1 +32.5 KB
Inhalt
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