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Zuletzt geändert von Holger Engels am 2026/03/17 21:52
Von Version 23.1
bearbeitet von Kim Fujan
am 2025/10/13 10:52
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Auf Version 49.1
bearbeitet von Holger Engels
am 2025/10/14 11:18
Änderungskommentar: Neuen Anhang Weiterzeichnen e.ggb hochladen

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7 7  [[Kompetenzen.K5]] Ich kann Ableitungsregeln zur Überprüfung anwenden
8 8  [[Kompetenzen.K5]] Ich kann die ln-Funktion als Stammfunktion von {{formula}}x\rightarrow\frac1x{{/formula}} nutzen {{niveau}}e{{/niveau}}
9 9  
10 +{{aufgabe id="Wanderung" afb="I" kompetenzen="K1" quelle="S.Kanzler; K.Fujan" cc="BY-SA" zeit="4" niveau="g"}}
11 +Soraya und Nico brechen beide zu einer Wanderung auf. Der erste Abschnitt ist jeweils im Grafen zu sehen. Diskutiere, ob es hinsichtlich der physischen Anstrengung einen Unterschied macht, dass Soraya im Gebirge und Nico von daheim aus startet.
12 +[[image:Wanderung.svg||style="display: block; margin: auto; width: 400px"]]
13 +{{/aufgabe}}
14 +
10 10  {{aufgabe id="Aufleiten ln" afb="III" kompetenzen="K5" tags="problemlösen" quelle="Dr. Andreas Dinh" cc="BY-SA" zeit="15" niveau="e"}}
11 11  Im Unterricht eines J2-Kurses soll die Funktion {{formula}}f(x)=\frac{1}{2x}{{/formula}} aufgeleitet werden. Johann rechnet mit der Kettenregel der Aufleitung wie folgt: {{formula}}F(x)=\frac{1}{2}\ln(|2x|){{/formula}}. Johannes mag die Kettenregel nicht und formt den Term von //f// zunächst um: {{formula}}f(x)=\frac{1}{2}\cdot\frac{1}{x}{{/formula}}, denn danach wird die Aufleitung ganz einfach: {{formula}}F(x)=\frac{1}{2}\ln(|x|){{/formula}}. Die beiden geraten in eine Diskussion darüber, welche Lösung richtig ist. Überprüfe dies.
12 12  {{/aufgabe}}
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18 18  1. Der Graph einer Stammfunktion von {{formula}}f{{/formula}} verläuft durch {{formula}}P{{/formula}}. Skizziere diesen Graphen in der Abbildung.
19 19  {{/aufgabe}}
20 20  
21 -{{aufgabe id="Stammfunktionen skizzieren" afb="II" kompetenzen="K5" tags="problemlösen" quelle="S.Kanzler; K.Fujan" cc="BY-SA" zeit="15" niveau="g"}}
26 +{{aufgabe id="Funktionen aus Ableitungsfunktionen skizzieren" afb="II" kompetenzen="K5" quelle="S.Kanzler; K.Fujan" cc="BY-SA" zeit="21" niveau="g"}}
22 22  
23 - Skizziere zu den abgebildeten Graphen jeweils die Stammfunktion.
24 - [[image:Parabel_aufl.PNG||width="180" style="float: left"]]
25 - [[image:x3_aufl.PNG||width="180" style="float: middle"]]
26 - [[image:x4_aufl.PNG||width="180" style="float: right"]]
28 + Skizziere zu den abgebildeten {{formula}}f'(x)-{{/formula}}Graphen jeweils die Orginalfunktion.
29 + [[image:Grafen_aufl.png||width="600" style="float: middle"]]
30 +
27 27  {{/aufgabe}}
28 28  
33 +{{aufgabe id="Funktionsgraph aus Eigenschaften" afb="II" kompetenzen=" " quelle="S.Kanzler, K.Fujan" cc="BY-SA" zeit="10"}}
34 +Über die Ableitungsfunktion {{formula}}f'(x){{/formula}} einer Polynomfunktion {{formula}}f(x){{/formula}} ist folgendes bekannt:
35 +* {{formula}}f'(x){{/formula}} hat eine Extremstelle bei {{formula}}x=1{{/formula}}
36 +* {{formula}}f'(-3)=f(3)=0{{/formula}}
37 +* {{formula}}f'(x){{/formula}} ist an der Stelle {{formula}}x=-3{{/formula}} linksgekrümmt
38 +
39 +(% class="abc" %)
40 +1. Bestimme den minimalen Grad der Ableitungsfunktion {{formula}}f'(x){{/formula}}.
41 +1. Skizziere ein passendes Schaubild der Ableitungsfunktion {{formula}}f'(x){{/formula}}.
42 +1. Ermittle dazu den Graph einer möglichen Funktion {{formula}}f(x){{/formula}}.
43 +{{/aufgabe}}
44 +
29 29  {{seitenreflexion/}}
30 30  
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XWiki.XWikiComments[0]
Autor
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1 +XWiki.fujan
Kommentar
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1 +Der Begriff "Stammfunktion" ist den SuS noch nicht bekannt, deshalb haben wir ihn auch vermieden.
Datum
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1 +2025-10-13 09:50:23.421