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Zuletzt geändert von Stephanie Wietzorek am 2025/05/21 10:29
Von Version 93.1
bearbeitet von Holger Engels
am 2025/05/21 07:13
Änderungskommentar: Neuen Anhang Ableitungsfunktion.ggb hochladen
Auf Version 108.1
bearbeitet von Stephanie Wietzorek
am 2025/05/21 10:27
Änderungskommentar: Neues Bild Arbeitsheft 6.3. Graphisches Differenzieren L2.svg hochladen

Zusammenfassung

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Dokument-Autor
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1 -XWiki.holgerengels
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Inhalt
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28 28  
29 29  {{aufgabe id="Punkte mit gegebener Steigung finden" afb="?" kompetenzen="" quelle="Stephanie Wietzorek und Simone Kanzler" cc="BY-SA" zeit="?"}}
30 30  Es ist das Schaubild {{formula}}K_f{{/formula}} einer Funktion {{formula}}f{{/formula}} gegeben. Kennzeichne Punkte auf {{formula}}K_f{{/formula}}, für die gilt:
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}}
31 +(%class=abc%)
32 +1. die Steigung der Tangente in diesem Punkt ist 1
33 +1. die Steigung der Tangente in diesem Punkt ist 1,5
34 +1. die Steigung der Tangente in diesem Punkt ist 0
35 +1. die Steigung der Tangente in diesem Punkt ist {{formula}}-\frac{17}{4}{{/formula}}
35 35  [[image:Tangentensteigung.svg|| width="700px"]]
36 36  {{/aufgabe}}
37 37  
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41 41  [[image:Schaubild.svg||width=500]]
42 42  {{/aufgabe}}
43 43  
44 -{{aufgabe id="Zuordnung I" afb="I" kompetenzen="" quelle="KMap" cc="BY-SA" zeit="4" interaktiv="Interaktiv Zuordnung"}}
45 +{{aufgabe id="Beschleunigung" afb="?" kompetenzen="" quelle="Stephanie Wietzorek, Simone Kanzler" cc="BY-SA" zeit="?"}}
46 +Ein Auto soll auf freier Autobahn auf {{formula}}180\frac{km}{h}{{/formula}} beschleunigen. Die Geschwindigkeit wird durch {{formula}}v(t)=180\cdot(1-e^{-0,1t}){{/formula}} beschrieben. {{formula}}v(t){{/formula}} beschreibt hierbei die momentante Geschwindigkeit zum Zeitpunkt {{formula}}t{{/formula}} in Sekunden. Der Verlauf der Geschwindigkeit ist dem Schaubild zu entnehmen.
47 +[[image:Beschleunigung.svg|| width="500px"]]
48 +
49 +(%class=abc%)
50 +1. Zu welchem Zeitpunkt wird die Höchstgeschwindigkeit von {{formula}}180\frac{km}{h}{{/formula}} erreicht?
51 +1. Wann ist die Beschleunigung am höchsten?
52 +1. Skizziere ein Schaubild, aus welchem die Beschleunigung zum Zeitpunkt t hervorgeht.
53 +{{/aufgabe}}
54 +
55 +{{aufgabe id="Zuordnung I" afb="I" kompetenzen="" quelle="KMap" cc="BY-SA" zeit="4" interaktiv="Interaktiv Zuordnung I"}}
45 45  (% style="float:left; margin-right: 16px" %)
46 46  | [[image:Polynome zuordnen f.svg||width=200]] | | | | | [[image:Polynome zuordnen A.svg||width=200]]
47 47  | [[image:Polynome zuordnen g.svg||width=200]] | | | | | [[image:Polynome zuordnen B.svg||width=200]]
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50 50  {{/aufgabe}}
51 51  
52 52  {{aufgabe id="Skizzieren anhand Eigenschaften" afb="?" kompetenzen="" quelle="Stephanie Wietzorek, Simone Kanzler" cc="BY-SA" zeit="4"}}
53 -a) Skizziere eine mögliche Parabel 2. Grades, welche eine waagrechte Tangente an der Stelle {{formula}}x = -2{{/formula}} hat. Welche Gemeinsamkeiten haben diese Parabeln?
54 -
55 -b) Skizziere das Schaubild einer möglichen Funktion, welches drei waagrechte Tangenten besitzt. Welchen minimalen Grad hat die Funktion?
56 -
57 -c) Eine Funktion f hat nur positive Steigungen. Skizziere das Schaubild der Ableitungsfunktion.
58 -
59 -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.
64 +(%class=abc%)
65 +1. Skizziere eine mögliche Parabel 2. Grades, welche eine waagrechte Tangente an der Stelle {{formula}}x = -2{{/formula}} hat. Welche Gemeinsamkeiten haben diese Parabeln?
66 +1. Skizziere das Schaubild einer möglichen Funktion, welches drei waagrechte Tangenten besitzt. Welchen minimalen Grad hat die Funktion?
67 +1. Eine Funktion f hat nur positive Steigungen. Skizziere das Schaubild der Ableitungsfunktion.
68 +1. 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.
60 60  (% class="border" %)
61 61  |x|-4|-1|0|1 |4
62 62  |Funktionswert|-2,5| |2 |0|
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93 93  ☐ Eine Sattelstelle kann auch eine Maximalstelle sein
94 94  {{/aufgabe}}
95 95  
96 -{{aufgabe id="Zuordnung II" afb="?" kompetenzen="" quelle="Stephanie Wietzorek, Simone Kanzler" cc="BY-SA" zeit="?"}}
97 -Es ist das Schaubild einer Steigungsfunktion gegeben. Zudem sind drei Schaubilder von drei Funktionen (A, B und C) gegeben. Welche Schaubilder (A, B oder C) können nicht zu der Steigungsfunktion gehören? Begründe deine Zuordnung.
98 -[[image:Ableitungsfunktion.svg|| width="500px"]]
99 -[[image:Ableitungsfunktion 1.svg||width="300px"]] [[image:Ableitungsfunktion 2.svg||width=300]] [[image:Ableitungsfunktion 3.svg||width=300]]
100 -{{/aufgabe}}
101 101  
106 +
102 102  {{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
Ableitungsfunktion 3.svg
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Arbeitsheft 6.3. Graphisches Differenzieren L1.ggb
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Arbeitsheft 6.3. Graphisches Differenzieren L2.ggb
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Arbeitsheft 6.3. Graphisches Differenzieren L2.svg
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Beschleunigung.ggb
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Beschleunigung.svg
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