Extremwertaufgaben: Unterschied zwischen den Versionen

aus ZUM-Wiki, dem Wiki für Lehr- und Lerninhalte auf ZUM.de
Wechseln zu: Navigation, Suche
(Visualisierung zur Überprüfung der Ergebnisse)
(Visualisierung zur Überprüfung der Ergebnisse)
Zeile 49: Zeile 49:
 
==Visualisierung zur Überprüfung der Ergebnisse==
 
==Visualisierung zur Überprüfung der Ergebnisse==
 
Bewege den roten Punkt, um die Groesse der Schachtel zu verändern
 
Bewege den roten Punkt, um die Groesse der Schachtel zu verändern
<ggb_applet width="1008" height="601"  version="4.0" ggbBase64="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" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" />
+
<ggb_applet width="1008" height="601"  version="4.0" ggbBase64="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" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" />
  
 
==Visualisiserung mit Tabelle==
 
==Visualisiserung mit Tabelle==

Version vom 31. Januar 2012, 21:03 Uhr

Inhaltsverzeichnis

Problemstellung

Der Goldfisch in Wermelskirchen möchte wiedereröffnen. Da es sich um einen Raucher-club handeln soll, hat der neue Inhaber sich überlegt, Streichholzschachteln als Werbung zu nutzen. Den Großteil seines Geldes hat er bereits in die Sanierung gesteckt, deshalb will er die Streichholzschachteln von seinen Mitarbeitern basteln lassen und zwar mit möglichst wenig Materialverbrauch. In einem Großmarkt hat der Besitzer dementspre-chend Pappe und Streichhölzer (4,5cm lang) gekauft. Einer der Mitarbeiter kam gestern mit folgender Bastelanleitung zu mir:

(Siehe Aufgabenblatt)

Er fragte mich, wie er aus der Pappe möglichst viele Streichholzschachteln basteln könnte. Als Vorgabe hat er gesagt bekommen, dass das Volumen 45cm³ haben muss. Könnt ihr ihm helfen, herauszufinden, welche Maße die Streichholzschachtel haben muss? (Die Klebekanten [siehe gestrichelte Linien] werden für die Berechnung nicht weiter berücksichtigt)

Falls du nicht weiterkommst: Hier findest du Hilfen

Hauptbedingung

 O=15a+20b+4ab

Nebenbedingung

 45=5ab

Zielfunktion

 O(a)=15a+180/a+36

Ableitung

 O'(a)=15+180/a^2

Notwendige Bedingung

 0=15+180/a^2

 a=3,46cm


Hinreichende Bedingung

 O''(3,46)>0 --> Tiefpunkt

Seitenlänge b und Oberfläche O

 b=2,6cm

 O=139,9cm^2

Randextrema

Sowohl fuer a gegen 0 als auch fuer a gegen unendlich, geht O(a) 
gegen unendlich --> 3,46 ist ein globales Minimum

Visualisierung zur Überprüfung der Ergebnisse

Bewege den roten Punkt, um die Groesse der Schachtel zu verändern

Visualisiserung mit Tabelle

Weiterführende Problemstellung

Bastel eine "optimale" Streichholzschachtel.

Überlege: Warum sind Streichholzschachteln in der Realität nicht "optimal"?

Verfasser

Team.gif
Entstanden unter Mitwirkung von:

Janina Wittenstein