Änderungen von Dokument BPE 12.7 Monotonie

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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		-
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"}}

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