Änderungen von Dokument BPE 12.1 Differentialquotient, Differenzierbarkeit

Zusammenfassung

• Seiteneigenschaften (1 geändert, 0 hinzugefügt, 0 gelöscht)
• Anhänge (0 geändert, 2 hinzugefügt, 0 gelöscht)
  • Differenzierbar Logarithmus.svg
  • Peter.svg

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Inhalt

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8	8	{{/aufgabe}}
9	9
10	10	{{aufgabe id="Blitzer" afb="" kompetenzen="" quelle="Kim Fujan" zeit="" cc="by-sa" tags=""}}
11		-Peter Planlos hat es, wie üblich, sehr eilig nach Hause zu kommen. Er braucht für eine 2,5 km lange Ortsdurchfahrt nur 3 Minuten und vergisst mal wieder, dass dort ein Blitzer steht. Nach 1,5 Minuten Fahrtzeit wird die Geschwindigkeit gemessen.
	11	+[[image:Peter.svg||style="float:right; width:350px"]]Peter Planlos hat es, wie üblich, sehr eilig nach Hause zu kommen. Er braucht für eine 2,5 km lange Ortsdurchfahrt nur 3 Minuten und vergisst mal wieder, dass dort ein Blitzer steht. Nach 1,5 Minuten Fahrtzeit wird die Geschwindigkeit gemessen.
12	12	Seine Zeit-Weg-Funktion ist durch {{formula}}f(t)=-\frac{5}{27}t^3+\frac{5}{6}t^2{{/formula}} gegeben.
13		-[[image:Peter.svg||style="float:right; width:350px"]]
14	14	(%class=abc%)
15	15	1. Berechne seine durchschnittliche Geschwindigkeit für die Ortsdurchfahrt.
16	16	1. Muss Peter jetzt mit einem Strafzettel rechnen? Erläutere!
17	17	{{/aufgabe}}
18	18
	18	+{{aufgabe id="Differentialquotient A" afb="II" kompetenzen="K5" quelle="Holger Engels, Kim Fujan" zeit="" cc="by-sa" tags=""}}
	19	+Berechne den Differentialquotienten an der Stelle {{formula}}x_0=1{{/formula}} für folgende Funktionen:
	20	+(%class=abc%)
	21	+1. {{formula}}f(x)=x^2+3{{/formula}}
	22	+1. {{formula}}f(x)=3\cdot x^2{{/formula}}
	23	+{{/aufgabe}}
	24	+
	25	+{{aufgabe id="Differentialquotient B" afb="III" kompetenzen="K5" quelle="Holger Engels, Kim Fujan" zeit="" cc="by-sa" tags=""}}
	26	+Berechne den Differentialquotienten für eine beliebige Stelle {{formula}}x_0{{/formula}} für folgende Funktionen:
	27	+(%class=abc%)
	28	+1. {{formula}}f(x)=x^2+3{{/formula}}
	29	+1. {{formula}}f(x)=3\cdot x^2{{/formula}}
	30	+1. {{formula}}f(x)=\sqrt(x){{/formula}}
	31	+{{/aufgabe}}
	32	+
19	19	{{seitenreflexion bildungsplan="3" kompetenzen="3" anforderungsbereiche="3" kriterien="3" menge="3"/}}

Differenzierbar Logarithmus.svg

Author

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	1	+XWiki.holgerengels

Größe

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	1	+13.8 KB

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Peter.svg

Author

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	1	+XWiki.holgerengels

Größe

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	1	+9.7 KB

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