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Zuletzt geändert von Stephanie Wietzorek am 2025/05/21 10:29
Von Version 47.2
bearbeitet von Holger Engels
am 2025/05/20 14:07
Änderungskommentar: Es gibt keinen Kommentar für diese Version
Auf Version 64.1
bearbeitet von Stephanie Wietzorek
am 2025/05/20 16:43
Änderungskommentar: Neues Bild Ableitungsfunktion 2.svg hochladen

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 ===
4 4  [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann Werte der Tangentensteigung graphisch bestimmen
5 5  [[Kompetenzen.K4]] [[Kompetenzen.K1]] Ich kann aus Werten der Tangentensteigung einen Graphen zeichnen und diesen als Graphen der Ableitungsfunktion deuten
6 6  [[Kompetenzen.K6]] Ich kann Zusammenhänge zwischen den beiden Funktionsgraphen beschreiben
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10 10  **Interaktiv Erkunden:** [[Graphisches Ableiten>>https://kmap.eu/app/browser/Mathematik/Differentialrechnung/Graphisches%20Ableiten#erkunden]]
11 11  {{/lernende}}
12 12  
13 -* Kann eine Tangente den Funktionsgraphen schneiden?
14 -
15 -* Bereiche mit positiver/ negativer Steigung schraffieren
16 16  * Punktweise graphisch ableiten
17 17  * Qualitativ graphisch ableiten
18 18  * Zusammenhänge HP, TP, SP vorwärts und rückwärts
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30 30  [[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"]]
31 31  {{/aufgabe}}
32 32  
33 -{{aufgabe id="Punkte mit gegebener Steigung finden" afb="?" kompetenzen="" quelle="Stephanie Wietzorek und Simone Kanzler" cc="BY-SA" zeit="3"}}
29 +{{aufgabe id="Punkte mit gegebener Steigung finden" afb="?" kompetenzen="" quelle="Stephanie Wietzorek und Simone Kanzler" cc="BY-SA" zeit="?"}}
34 34  Es ist das Schaubild {{formula}}K_f{{/formula}} einer Funktion {{formula}}f{{/formula}} gegeben. Kennzeichne Punkte auf {{formula}}K_f{{/formula}}, für die gilt:
35 - {{formula}}f'(x) =1{{/formula}}
36 - {{formula}}f'(x) =1,5{{/formula}}
37 - {{formula}}f'(x) =0{{/formula}}
38 - {{formula}}f'(x) = -\frac{17}{4}{{/formula}}
31 + die Steigung der Tangente in diesem Punkt ist 1
32 + die Steigung der Tangente in diesem Punkt ist 1,5
33 + die Steigung der Tangente in diesem Punkt ist 0
34 + die Steigung der Tangente in diesem Punkt ist {{formula}}-\frac{17}{4}{{/formula}}
39 39  [[image:Tangentensteigung.svg|| width="700px"]]
40 40  {{/aufgabe}}
41 41  
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47 47  | [[image:Polynome zuordnen i.svg||width=200]] | | | | | [[image:Polynome zuordnen D.svg||width=200]]
48 48  {{/aufgabe}}
49 49  
50 -{{aufgabe id="Skizzieren anhand Eigenschaften" afb="?" kompetenzen="" quelle=" Stephanie Wietzorek, Simone Kanzler" cc="BY-SA" zeit="4" interaktiv="Interaktiv Zuordnung"}}
51 -(% style="float:left; margin-right: 16px" %)
52 -Es ist ein zur y-Achse symmetrisches Schaubild einer Funktion 4. Grades gesucht. Folgende Angaben sind bekannt:
46 +{{aufgabe id="Skizzieren anhand Eigenschaften" afb="?" kompetenzen="" quelle="Stephanie Wietzorek, Simone Kanzler" cc="BY-SA" zeit="4"}}
47 +a) Skizziere eine mögliche Parabel 2. Grades, welche eine waagrechte Tangente an der Stelle {{formula}}x = -2{{/formula}} hat. Welche Gemeinsamkeiten haben diese Parabeln?
53 53  
49 +b) Skizziere das Schaubild einer möglichen Funktion, welches drei waagrechte Tangenten besitzt. Welchen minimalen Grad hat die Funktion?
50 +
51 +c) Eine Funktion f hat nur positive Steigungen. Skizziere das Schaubild der Ableitungsfunktion.
52 +
53 +d) Es ist ein zur y-Achse symmetrisches Schaubild einer Funktion 4. Grades gesucht. Folgende Angaben sind bekannt, fülle die Lücken und skizziere das Schaubild der Funktion.
54 54  (% class="border" %)
55 -|= {{formula}}x{{/formula}} |-4|-1|0|1 |4
56 -|= {{formula}}f(x){{/formula}} |-2,5| |2 |0|
57 -|= {{formula}}f'(x){{/formula}} |-2| |0|-1 |
55 +|x|-4|-1|0|1 |4
56 +|Funktionswert|-2,5| |2 |0|
57 +|Tangentensteigung|-2| |0|-1 |
58 58  {{/aufgabe}}
59 59  
60 -{{aufgabe id="Aussagen" afb="I" kompetenzen="" quelle="KMap" cc="BY-SA" zeit="3"}}
60 +{{aufgabe id="Aussagen Polynomfunktion" afb="I" kompetenzen="" quelle="KMap" cc="BY-SA" zeit="3"}}
61 61  Prüfe die Aussagen! Welche sind wahr? Eine Polynomfunktion 3. Grades ..
62 62  ☐ hat immer zwei Extrempunkte!
63 63  ☐ kann auch mal nur einen Extrempunkt haben!
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66 66  ☐ hat entweder einen Sattelpunkt oder zwei Extrempunkte!
67 67  {{/aufgabe}}
68 68  
69 +{{aufgabe id="Aussagen Schaubild" afb="?" kompetenzen="" quelle="Stephanie Wietzorek, Simone Kanzler" cc="BY-SA" zeit="?"}}
70 +Gegeben ist das Schaubild einer Funktion. Nimm Stellung zu folgenden Aussagen und begründe deine Antwort.
71 +[[image:Aussagen.svg|| width="500px"]]
72 +☐ {{formula}}f(-3)=3{{/formula}}
73 +☐ {{formula}}x = 3{{/formula}} ist dreifache Nullstell
74 +☐ die Tangentensteigungen sind negativ für {{formula}}x \in ]2;5[{{/formula}}
75 +☐ die Steigung der Tangente an der Stelle {{formula}}x = 1<-2{{/formula}}
76 +☐ an der Stelle {{formula}}x = 2{{/formula}} liegt eine waagrechte Tangente
77 +☐ die Tangentensteigungen sind negativ für {{formula}}-4 < x < 2{{/formula}}
78 +☐ die Tangentensteigungen haben einen Vorzeichenwechsel bei {{formula}}x=-4{{/formula}} von ⊝ ⇾ ⊕
79 +{{/aufgabe}}
80 +
81 +{{aufgabe id="Aussagen Sattelstelle" afb="I" kompetenzen="" quelle="KMap" cc="BY-SA" zeit="3"}}
82 +Welche Aussagen treffen auf eine Sattelstelle zu?
83 +☐ Eine Sattelstelle hat eine waagrechte Asymptote
84 +☐ An einer Sattelstelle hat die Steigung ein Maximum oder ein Minimum
85 +☐ An einer Sattelstelle gibt es immer auch einen Krümmungswechsel
86 +☐ Eine Sattelstelle ist auch eine Wendestelle
87 +☐ Eine Sattelstelle kann auch eine Maximalstelle sein
88 +{{/aufgabe}}
89 +
69 69  {{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
Ableitungsfunktion 1.svg
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Ableitungsfunktion 2.svg
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