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Zuletzt geändert von Holger Engels am 2025/10/15 06:54
Von Version 42.1
bearbeitet von Kim Fujan
am 2025/10/13 10:13
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Auf Version 70.1
bearbeitet von Holger Engels
am 2025/10/15 06:53
Änderungskommentar: Neues Bild Aufleiten F.svg hochladen

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Dokument-Autor
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1 -XWiki.fujan
1 +XWiki.holgerengels
Inhalt
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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" tags="problemlösen" quelle="S.Kanzler; K.Fujan" cc="BY-SA" zeit="4" niveau="g"}}
11 -
12 -Soraya und Nico bewältigen beide auf einer Wanderung eine Steigung von 30%. Nico startet dabei vor seiner Haustür und Soraya ist im Hochgebirge unterwegs. Begründe, warum die Leistung der beiden vergleichbar ist.
13 -
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"]]
14 14  {{/aufgabe}}
15 15  
16 -
17 17  {{aufgabe id="Aufleiten ln" afb="III" kompetenzen="K5" tags="problemlösen" quelle="Dr. Andreas Dinh" cc="BY-SA" zeit="15" niveau="e"}}
18 18  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.
19 19  {{/aufgabe}}
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25 25  1. Der Graph einer Stammfunktion von {{formula}}f{{/formula}} verläuft durch {{formula}}P{{/formula}}. Skizziere diesen Graphen in der Abbildung.
26 26  {{/aufgabe}}
27 27  
28 -{{aufgabe id="Funktionen aus Ableitungsfunktionen skizzieren" afb="II" kompetenzen="K5" tags="problemlösen" quelle="S.Kanzler; K.Fujan" cc="BY-SA" zeit="21" niveau="g"}}
29 -
30 - Skizziere zu den abgebildeten {{formula}}f'(x)-{{/formula}}Graphen jeweils die Orginalfunktion.
31 - [[image:Grafen_aufl.png||width="600" style="float: middle"]]
32 -
26 +{{aufgabe id="Graphisch aufleiten" afb="II" kompetenzen="K5" quelle="S.Kanzler; K.Fujan" cc="BY-SA" zeit="21" niveau="g"}}
27 +Skizziere zu den abgebildeten {{formula}}f'(x){{/formula}}-Graphen jeweils den der Orginalfunktion.
28 +[[image:Aufleiten A.svg||width="350"]][[image:Aufleiten B.svg||width="350"]][[image:Aufleiten C.svg||width="350"]][[image:Aufleiten D.svg||width="350"]][[image:Aufleiten E.svg||width="350"]][[image:Aufleiten F.svg||width="350"]]
33 33  {{/aufgabe}}
34 34  
35 -{{aufgabe id="Funktionsgraph aus Eigenschaften" afb="II" kompetenzen=" " quelle="S.Kanzler, K.Fujan" cc="BY-SA" zeit="5"}}
36 -Über die Ableitungsfunktion {{formula}}f'(x){{/formula}} einer Funktion {{formula}}f(x){{/formula}} ist folgendes bekannt:
31 +{{aufgabe id="Funktionsgraph aus Eigenschaften" afb="II" kompetenzen=" " quelle="S.Kanzler, K.Fujan" cc="BY-SA" zeit="10"}}
32 +Über die Ableitungsfunktion {{formula}}f'(x){{/formula}} einer Polynomfunktion {{formula}}f(x){{/formula}} ist folgendes bekannt:
37 37  * {{formula}}f'(x){{/formula}} hat eine Extremstelle bei {{formula}}x=1{{/formula}}
38 38  * {{formula}}f'(-3)=f(3)=0{{/formula}}
39 39  * {{formula}}f'(x){{/formula}} ist an der Stelle {{formula}}x=-3{{/formula}} linksgekrümmt
40 -
36 +
41 41  (% class="abc" %)
42 -1. Bestimme den Grad der Ableitungsfunktion {{formula}}f'(x){{/formula}}.
38 +1. Bestimme den minimalen Grad der Ableitungsfunktion {{formula}}f'(x){{/formula}}.
43 43  1. Skizziere ein passendes Schaubild der Ableitungsfunktion {{formula}}f'(x){{/formula}}.
44 44  1. Ermittle dazu den Graph einer möglichen Funktion {{formula}}f(x){{/formula}}.
45 45  {{/aufgabe}}
46 46  
43 +{{aufgabe id="Weiterzeichnen Exponentialfunktion" afb="II" kompetenzen="K4" quelle="Simone Kanzler" zeit="5" cc="by-sa" tags=""niveau="e"}}
44 +Gegeben sind Ausschnitte der Schaubilder der Funktionen //f// und //f'//. Ergänze die beiden Schaubilder im Bereich {{formula}}[-3; 6]{{/formula}}.
45 +[[image:Weiterzeichnen e.svg||style="margin:auto; width:500px"]]
46 +{{/aufgabe}}
47 +
48 +{{aufgabe id="Weiterzeichnen Polynomfunktion" afb="II" kompetenzen="K4" quelle="Simone Kanzler" zeit="5" cc="by-sa" tags=""niveau="e"niveau="e"}}
49 +Gegeben sind Ausschnitte der Schaubilder der Funktionen //f// und //f'//. Ergänze die beiden Schaubilder im Bereich {{formula}}[-4; 4]{{/formula}}.
50 +[[image:Weiterzeichnen p.svg||style="margin:auto; width:500px"]]
51 +{{/aufgabe}}
52 +
47 47  {{seitenreflexion/}}
48 48  
Aufleiten A.svg
Author
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1 +XWiki.holgerengels
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Aufleiten C.svg
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