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Zuletzt geändert von Stephanie Wietzorek am 2025/05/21 10:29
Von Version 94.1
bearbeitet von Holger Engels
am 2025/05/21 07:13
Änderungskommentar: Neues Bild Ableitungsfunktion 3.svg hochladen
Auf Version 99.1
bearbeitet von Stephanie Wietzorek
am 2025/05/21 09:45
Änderungskommentar: Neues Bild Beschleunigung.svg hochladen

Zusammenfassung

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1 -XWiki.holgerengels
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Inhalt
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16 16  * Funktionsterm der Ableitungsfunktion aus Tangentensteigungen aufstellen
17 17  * Beobachtungen bei e^x
18 18  
19 +{{aufgabe id="Beschleunigung" afb="?" kompetenzen="" quelle="Stephanie Wietzorek, Simone Kanzler" cc="BY-SA" zeit="?"}}
20 +Ein Auto soll auf freier Autobahn auf {{formula}}180/frac{km}{h}{{/formula}} beschleunigen. Die Geschwindigkeit wird durch {{formula}}v(t)=180\cdot(1-\exp{-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.
21 +[[image:Beschleunigung.svg|| width="500px"]]
22 +
23 +(%class=abc%)
24 +1. Zu welchem Zeitpunkt wird die Höchstgeschwindigkeit von {{formula}}180/frac{km}{h}{{/formula}} erreicht?
25 +1. Wann ist die Beschleunigung am höchsten?
26 +1. Skizziere ein Schaubild, aus welchem die Beschleunigung zum Zeitpunkt t hervorgeht.
27 +{{/aufgabe}}
28 +
19 19  {{aufgabe id="Tangenten einzeichnen" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA" zeit="3"}}
20 20  Zeichne jeweils die Tangenten an den Stellen {{formula}}x\in\{-1, 0, 1\}{{/formula}} ein und bestimme deren Steigungen.
21 21  [[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"]]
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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"}}
54 +{{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.
63 +(%class=abc%)
64 +1. Skizziere eine mögliche Parabel 2. Grades, welche eine waagrechte Tangente an der Stelle {{formula}}x = -2{{/formula}} hat. Welche Gemeinsamkeiten haben diese Parabeln?
65 +1. Skizziere das Schaubild einer möglichen Funktion, welches drei waagrechte Tangenten besitzt. Welchen minimalen Grad hat die Funktion?
66 +1. Eine Funktion f hat nur positive Steigungen. Skizziere das Schaubild der Ableitungsfunktion.
67 +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  
105 +
102 102  {{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
Beschleunigung.ggb
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Beschleunigung.svg
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