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Änderungen von Dokument BPE 12.7 Monotonie

Zuletzt geändert von Holger Engels am 2025/12/22 17:55
Von Version 12.1
bearbeitet von Ingrid Kolupa
am 2025/10/13 15:16
Änderungskommentar: Es gibt keinen Kommentar für diese Version
Auf Version 57.1
bearbeitet von Holger Engels
am 2025/12/22 17:54
Änderungskommentar: Neues Bild Ableitungsgraph.svg hochladen

Zusammenfassung

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Dokument-Autor
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1 -XWiki.ingridkolupa
1 +XWiki.holgerengels
Inhalt
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3 3  [[Kompetenzen.K5]] [[Kompetenzen.K4]] Ich kann Funktionen auf strenge Monotonie untersuchen
4 4  [[Kompetenzen.K4]] Ich kann die Wertemenge einer Funktion anhand von Graphen, Funktionstermen und Wertetabellen bestimmen
5 5  
6 -{{aufgabe id="Monotonie mit Hilfe des Schaubilds der Ableitung ermitteln" afb="I" kompetenzen="K1, K4" quelle="Ingrid Kolupa, Katharina Justice" zeit="5" cc="by-sa" tags=""}}
7 -Gegeben ist der Graph von {{formula}}f'(x){{/formula}}.
8 -[[image:Ableitungsgraph.svg]]
9 -1. In welchen Bereichen ist {{formula}}f(x){{/formula}} monoton steigend?
10 -1.
11 -1. Listenpunkt
6 +{{aufgabe id="Monotoniebereiche bestimmen" afb="II" kompetenzen="K1, K4" quelle="Simone Kanzler" zeit="10" cc="by-sa" tags=""}}
7 +Gib die Monotoniebereiche der Funktionen {{formula}}f(x){{/formula}} an:
8 +(%class=abc%)
9 +1. {{formula}}f(x)=\frac{1}{8}(\frac{1}{3}x^3+\frac{5}{2}x^2-50x+32){{/formula}}
10 +1. {{formula}}g(x)=e^{(2x+1)}(x-1){{/formula}}
11 +1. {{formula}}h(x)=ae^{(-x-5)}x^2{{/formula}}
12 +{{/aufgabe}}
12 12  
14 +{{aufgabe id="Skizzieren mithilfe der Monotonie" afb="II" kompetenzen="K1, K4" quelle="Simone Kanzler" zeit="9" cc="by-sa" tags=""}}
15 +Gegeben sind folgende Aussagen über die Funktion {{formula}}f(x){{/formula}}:
16 +1. Für {{formula}}x \in [-\infty;-3]{{/formula}} gilt: {{formula}}f’(x){{/formula}}>0
17 +1. Für {{formula}}x \in [-3;2]{{/formula}} gilt: {{formula}}f’(x){{/formula}}<0
18 +1. Für {{formula}}x \to \infty{{/formula}} gilt:{{formula}} f(x) \to 0{{/formula}}.
13 13  
20 +(%class=abc%)
21 +1. Gib für jede Aussage das entsprechende Monotonieverhalten an.
22 +1. Skizziere mithilfe der Aussagen ein mögliches Schaubild der Funktion {{formula}}f(x){{/formula}}.
23 +{{/aufgabe}}
14 14  
25 +{{aufgabe id="Aus Schaubild der Ableitung" afb="II" kompetenzen="K1, K4" quelle="Ingrid Kolupa, Katharina Justice" zeit="10" cc="by-sa" tags=""}}
26 +[[image:Ableitungsgraph.svg||class="right" width=350]]Gegeben ist der Graph von {{formula}}f'(x){{/formula}}.
27 +Beurteile die folgenden Aussagen:
28 +(%class=abc%)
29 +1. Für {{formula}}x \in [2;3]{{/formula}} ist der Graph von //f// monoton fallend.
30 +1. Zwischen dem Hochpunkt und dem Tiefpunkt des Graphen von {{formula}}f'{{/formula}} ist der Graph der Funktion //f// monoton fallend.
31 +1. Es gilt: {{formula}}f(-2)<f(0){{/formula}}
32 +1. Für {{formula}}x<-2{{/formula}} gilt: {{formula}}f''(x) > 0{{/formula}}
15 15  {{/aufgabe}}
16 16  
17 17  {{aufgabe id="Monotonie" afb="II" kompetenzen="K2, K1, K5" tags="problemlösen" quelle="Dr. Andreas Dinh" cc="BY-SA" zeit="25"}}
Ableitungsgraph.svg
Author
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1 -XWiki.ingridkolupa
1 +XWiki.holgerengels
Größe
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1 -14.1 KB
1 +10.8 KB
Inhalt
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