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Änderungen von Dokument BPE 12.7 Monotonie

Zuletzt geändert von Holger Engels am 2025/12/22 17:55
Von Version 57.2
bearbeitet von Holger Engels
am 2025/12/22 17:55
Änderungskommentar: Es gibt keinen Kommentar für diese Version
Auf Version 55.2
bearbeitet von Holger Engels
am 2025/11/21 22:29
Änderungskommentar: Es gibt keinen Kommentar für diese Version

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11 11  1. {{formula}}h(x)=ae^{(-x-5)}x^2{{/formula}}
12 12  {{/aufgabe}}
13 13  
14 -{{aufgabe id="Skizzieren mithilfe der Monotonie" afb="II" kompetenzen="K1, K4" quelle="Simone Kanzler" zeit="9" cc="by-sa" tags=""}}
14 +{{aufgabe id="Schaubild skizzieren mithilfe der Monotonie" afb="II" kompetenzen="K1, K4" quelle="Simone Kanzler" zeit="9" cc="by-sa" tags=""}}
15 15  Gegeben sind folgende Aussagen über die Funktion {{formula}}f(x){{/formula}}:
16 +(%class=abc%)
16 16  1. Für {{formula}}x \in [-\infty;-3]{{/formula}} gilt: {{formula}}f’(x){{/formula}}>0
17 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}}.
19 +1. Für {{formula}} x \to \infty{{/formula}} gilt:{{formula}} f(x) \to 0{{/formula}}.
19 19  
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}}.
21 +a) Gib für jede Aussage das entsprechende Monotonieverhalten an.
22 +b) Skizziere mithilfe der Aussagen ein mögliches Schaubild der Funktion {{formula}}f(x){{/formula}}.
23 +
23 23  {{/aufgabe}}
24 24  
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'{{/formula}}.
27 -
26 +{{aufgabe id="Monotonie mit Hilfe des Schaubilds der Ableitung ermitteln" afb="II" kompetenzen="K1, K4" quelle="Ingrid Kolupa, Katharina Justice" zeit="10" cc="by-sa" tags=""}}
27 +Gegeben ist der Graph von {{formula}}f'(x){{/formula}}.
28 +[[image:Ableitungsgraph.svg]]
28 28  Beurteile die folgenden Aussagen:
29 29  (%class=abc%)
30 -1. Für {{formula}}x \in [2;3]{{/formula}} ist der Graph von {{formula}}f{{/formula}} monoton fallend.
31 -1. Zwischen dem Hochpunkt und dem Tiefpunkt des Graphen von {{formula}}f'{{/formula}} ist der Graph der Funktion {{formula}}f{{/formula}} monoton fallend.
31 +1. Für {{formula}}x \in [2;3]{{/formula}} ist der Graph von f monoton fallend.
32 +1. Zwischen dem Hochpunkt und dem Tiefpunkt des Graphen von {{formula}}f'(x){{/formula}} ist der Graph der Funktion {{formula}}f(x){{/formula}} monoton fallend.
32 32  1. Es gilt: {{formula}}f(-2)<f(0){{/formula}}
33 33  1. Für {{formula}}x<-2{{/formula}} gilt: {{formula}}f''(x) > 0{{/formula}}
34 34  {{/aufgabe}}
Ableitungsgraph.ggb
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Ableitungsgraph.svg
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