{"introPage":{"showIntroPage":false,"startButtonText":"Starte Quiz","introduction":""},"progressType":"dots","passPercentage":50,"questions":[{"params":{"media":{"disableImageZooming":false},"text":"

Bestimme jeweils den Differenzenquotienten der Funktion f im Intervall I.<\/p>\n","overallFeedback":[{"from":0,"to":100}],"showSolutions":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","checkAnswer":"\u00dcberpr\u00fcfen","notFilledOut":"Bitte f\u00fclle alle L\u00fccken aus, um die L\u00f6sung ansehen zu k\u00f6nnen","answerIsCorrect":"':ans' ist korrekt","answerIsWrong":"':ans' ist falsch","answeredCorrectly":"Korrekt beantwortet","answeredIncorrectly":"Falsch beantwortet","solutionLabel":"Korrekte Antwort:","inputLabel":"L\u00fccke @num von @total","inputHasTipLabel":"Tipp verf\u00fcgbar","tipLabel":"Tipp","behaviour":{"enableRetry":false,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":true},"scoreBarLabel":"Du hast :num von :total Punkten erreicht.","confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"questions":["

a) \\( f(x) = x\u00b2 + 1 \\) I = [0;2] Differenzenquotient = *2*<\/p>\n\n

b) \\( f(x) = \\sqrt{x} \\) I = [0;4] Differenzenquotient = *0,5\/0.5*<\/p>\n\n

c) \\( f(x) = \\frac{1}{x} \\) I = [0,5;1] Differenzenquotient = *-2*<\/p>\n\n

d) \\( f(x) = \\sqrt{x+3} - x \\) I = [1;6] Differenzenquotient = *-0,8\/-0.8*<\/p>\n\n

<\/p>\n\n

F\u00fclle die L\u00fccken aus.<\/p>\n","overallFeedback":[{"from":0,"to":100}],"showSolutions":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","checkAnswer":"\u00dcberpr\u00fcfen","notFilledOut":"Bitte f\u00fclle alle L\u00fccken aus, um die L\u00f6sung ansehen zu k\u00f6nnen","answerIsCorrect":"':ans' ist korrekt","answerIsWrong":"':ans' ist falsch","answeredCorrectly":"Korrekt beantwortet","answeredIncorrectly":"Falsch beantwortet","solutionLabel":"Korrekte Antwort:","inputLabel":"L\u00fccke @num von @total","inputHasTipLabel":"Tipp verf\u00fcgbar","tipLabel":"Tipp","behaviour":{"enableRetry":false,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":true},"scoreBarLabel":"Du hast :num von :total Punkten erreicht.","confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"questions":["

a) Den Term \\( \\frac{f(x) - f(a)}{x - a} \\) nennt man *Differenzenquotient* oder mittlere *\u00c4nderungsrate* von f im Intervall [a; x].<\/p>\n\n

Er entspricht im Graphen der *Steigung* der Sekante durch die Punkte A( a | f(a) ) und P( x | f(x) ).
\n <\/p>\n\n

b) Wenn \\( \\frac{f(x) - f(a)}{x - a} \\) f\u00fcr x \u2192 *a* gegen einen Grenzwert strebt, so hei\u00dft dieser
\n
\n *Ableitung* oder *momentane* \u00c4nderungsrate von f an der Stelle a.<\/p>\n\n

Diese ist die Steigung der *Tangente* an den Graphen von f im Punkt A( a | f(a) ).<\/p>\n\n

<\/p>\n\n

Berechne den jeweiligen Wert der Ableitung.<\/p>\n","overallFeedback":[{"from":0,"to":100}],"showSolutions":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","checkAnswer":"\u00dcberpr\u00fcfen","notFilledOut":"Bitte f\u00fclle alle L\u00fccken aus, um die L\u00f6sung ansehen zu k\u00f6nnen","answerIsCorrect":"':ans' ist korrekt","answerIsWrong":"':ans' ist falsch","answeredCorrectly":"Korrekt beantwortet","answeredIncorrectly":"Falsch beantwortet","solutionLabel":"Korrekte Antwort:","inputLabel":"L\u00fccke @num von @total","inputHasTipLabel":"Tipp verf\u00fcgbar","tipLabel":"Tipp","behaviour":{"enableRetry":false,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":true},"scoreBarLabel":"Du hast :num von :total Punkten erreicht.","confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"questions":["

a) \\( f(x) = x\u00b2 + 1 \\) f '(1) = *2*<\/p>\n\n

b) \\( f(x) = 2x\u00b3 - x\u00b2 + 3x - 5 \\) f '(2) = *23*<\/p>\n\n

c) \\( f(x) = \\frac{4}{x^{2}} \\) f '(2) = *-1*<\/p>\n\n

d) \\( f(x) = 4\\sqrt{x} + x \\) f '(4) = *2*<\/p>\n\n

<\/p>\n\n

a) \\( f(x) = x^{11} \\) f '(1) = *11*<\/p>\n\n

b) \\( f(x) = x\u00b3 - 2x\u00b2 + x - 3 \\) f '(-1) = *8*<\/p>\n\n

c) \\( f(x) = \\frac{1}{x^{3}} \\) f '(1) = *-3*<\/p>\n\n

d) \\( f(x) = \\sqrt{2}x^2 + 5 \\) f '(0) = *0*<\/p>\n\n

<\/p>\n\n

f = g + h \u21d2 f '(x) = g'(x) + h'(x) <\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

f = g - h \u21d2 f '(x) = g'(x) - h'(x) <\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

f = g \u00b7 h \u21d2 f '(x) = g'(x) \u00b7 h'(x) <\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

f = g : h \u21d2 f '(x) = g'(x) : h'(x) <\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

f = c \u00b7 g \u21d2 f '(x) = c' \u00b7 g'(x)<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

f = c \u00b7 g \u21d2 f '(x) = c \u00b7 g'(x)<\/div>\n"}],"overallFeedback":[{"from":0,"to":100}],"behaviour":{"enableRetry":false,"enableSolutionsButton":true,"enableCheckButton":true,"type":"auto","singlePoint":false,"randomAnswers":false,"showSolutionsRequiresInput":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false,"passPercentage":100,"showScorePoints":true},"UI":{"checkAnswerButton":"\u00dcberpr\u00fcfen","showSolutionButton":"L\u00f6sung anzeigen","tryAgainButton":"Wiederholen","tipsLabel":"Hinweis anzeigen","scoreBarLabel":"Du hast :num von :total Punkten erreicht.","tipAvailable":"Hinweis verf\u00fcgbar","feedbackAvailable":"R\u00fcckmeldung verf\u00fcgbar","readFeedback":"R\u00fcckmeldung vorlesen","wrongAnswer":"Falsche Antwort","correctAnswer":"Richtige Antwort","shouldCheck":"H\u00e4tte gew\u00e4hlt werden m\u00fcssen","shouldNotCheck":"H\u00e4tte nicht gew\u00e4hlt werden sollen","noInput":"Bitte antworte, bevor du die L\u00f6sung ansiehst","a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Auswahlen werden als richtig, falsch oder fehlend markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtigen L\u00f6sungen werden in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Versuche werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet."},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"

g und h sind zwei beliebige Funktionen, c \u2208\u211d ist eine Konstante.
\nKreuze die wahren Aussagen an.<\/p>\n"},"library":"H5P.MultiChoice 1.14","metadata":{"contentType":"Multiple Choice","license":"U","title":"Faktor- und Summenregel","defaultLanguage":"de"},"subContentId":"22e3e733-245c-4261-9e1a-778137c759b1"},{"params":{"media":{"disableImageZooming":false,"type":{"params":{"contentName":"Bild","file":{"path":"images\/file-5eea3f9e9dc1b.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":370,"height":332}},"library":"H5P.Image 1.1","metadata":{"contentType":"Image","license":"U","title":"Unbenannt: Image","defaultLanguage":"de"},"subContentId":"f3a563e9-4e4c-4f6b-8334-3ad0015875d2"}},"text":"

Die Abbildung zeigt den Graphen der Funktion f und den Graphen der Ableitungsfunktion f '. F\u00fclle die L\u00fccken aus.<\/p>\n","overallFeedback":[{"from":0,"to":100}],"showSolutions":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","checkAnswer":"\u00dcberpr\u00fcfen","notFilledOut":"Bitte f\u00fclle alle L\u00fccken aus, um die L\u00f6sung ansehen zu k\u00f6nnen","answerIsCorrect":"':ans' ist korrekt","answerIsWrong":"':ans' ist falsch","answeredCorrectly":"Korrekt beantwortet","answeredIncorrectly":"Falsch beantwortet","solutionLabel":"Korrekte Antwort:","inputLabel":"L\u00fccke @num von @total","inputHasTipLabel":"Tipp verf\u00fcgbar","tipLabel":"Tipp","behaviour":{"enableRetry":false,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":true},"scoreBarLabel":"Du hast :num von :total Punkten erreicht.","confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"questions":["

a) f(0) = *-1*<\/p>\n\n

b) f '(1) = *-1*<\/p>\n\n

c) f '(x) = 0 \u21d4 x = *0\/1,5\/1.5* oder x = *0\/1,5\/1.5*<\/p>\n\n

d) Die Steigung von f ist positiv f\u00fcr f\u00fcr x > *1,5\/1.5*<\/p>\n\n

<\/p>\n\n

<\/p>\n"],"a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Eingaben werden als richtig, falsch oder unbeantwortet markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtigen L\u00f6sungen werden in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Eingaben werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet.","a11yCheckingModeHeader":"\u00dcberpr\u00fcfen-Modus aktiv"},"library":"H5P.Blanks 1.12","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"Graph und Ableitungsgraph","defaultLanguage":"de"},"subContentId":"6f5e2706-2615-4d34-93f9-6325a6644a12"},{"params":{"media":{"type":{"params":{"contentName":"Bild","file":{"path":"images\/file-5ef5d448d303f.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":298,"height":343}},"library":"H5P.Image 1.1","metadata":{"contentType":"Image","license":"U","title":"Unbenannt: Image","defaultLanguage":"de"},"subContentId":"614511a0-2bb4-4db9-9702-1b4a89e7294d"},"disableImageZooming":false},"answers":[{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

f '(0) = f(0) = 0<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

f ' hat mindestens 3 Nullstellen<\/div>\n"},{"correct":false,"tipsAndFeedback":{"chosenFeedback":"

F\u00fcr x \u2265 0 sind die Funktionswerte von f gr\u00f6\u00dfergleich 0, die Steigung nimmt jedoch auch telweise negative Werte an.<\/div>\n","tip":"","notChosenFeedback":""},"text":"

F\u00fcr x \u2265 0 ist f(x)' \u2265 0<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

F\u00fcr x \u2264 -1 ist f(x)' \u2264 0<\/div>\n"},{"correct":false,"tipsAndFeedback":{"chosenFeedback":"

Es gilt f (-1) = 0 aber f '(-1) < 0.<\/div>\n","tip":"","notChosenFeedback":""},"text":"

f '(-1) = 0.<\/div>\n"}],"overallFeedback":[{"from":0,"to":100}],"behaviour":{"enableRetry":false,"enableSolutionsButton":true,"enableCheckButton":true,"type":"auto","singlePoint":false,"randomAnswers":false,"showSolutionsRequiresInput":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false,"passPercentage":100,"showScorePoints":true},"UI":{"checkAnswerButton":"\u00dcberpr\u00fcfen","showSolutionButton":"L\u00f6sung anzeigen","tryAgainButton":"Wiederholen","tipsLabel":"Hinweis anzeigen","scoreBarLabel":"Du hast :num von :total Punkten erreicht.","tipAvailable":"Hinweis verf\u00fcgbar","feedbackAvailable":"R\u00fcckmeldung verf\u00fcgbar","readFeedback":"R\u00fcckmeldung vorlesen","wrongAnswer":"Falsche Antwort","correctAnswer":"Richtige Antwort","shouldCheck":"H\u00e4tte gew\u00e4hlt werden m\u00fcssen","shouldNotCheck":"H\u00e4tte nicht gew\u00e4hlt werden sollen","noInput":"Bitte antworte, bevor du die L\u00f6sung ansiehst","a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Auswahlen werden als richtig, falsch oder fehlend markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtigen L\u00f6sungen werden in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Versuche werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet."},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"

Die Abbildung zeigt den Graphen einer Funktion f. Kreuze die wahren Aussagen an.<\/p>\n"},"library":"H5P.MultiChoice 1.14","metadata":{"contentType":"Multiple Choice","license":"U","title":"Ableitung 1","defaultLanguage":"de"},"subContentId":"2d217c50-0abe-4951-bb1f-da7d8c18633d"},{"params":{"scoreShow":"\u00dcberpr\u00fcfen","tryAgain":"Wiederholen","scoreExplanation":"Richtige Antworten geben +1 Punkte. Bei falschen Antworten gibt es -1 Punkt. Die kleinstm\u00f6gliche Punktzahl ist 0.","question":{"settings":{"size":{"width":620,"height":310}},"task":{"elements":[{"x":50.08077544426494,"y":61.29032258064516,"width":8.666061268174474,"height":6.788032189014539,"dropZones":["0","1","2","3"],"type":{"library":"H5P.Image 1.1","params":{"contentName":"Bild","file":{"path":"images\/file-5ef9f80d2bfcb.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":744,"height":699},"alt":"Graph von f"},"subContentId":"e3397054-5bd6-4a47-8239-b51e6758f5c8","metadata":{"contentType":"Image","license":"U","title":"Unbenannt: Image","defaultLanguage":"de"}},"backgroundOpacity":100,"multiple":false},{"x":78.99838449111469,"y":51.61290322580645,"width":7.414041882067851,"height":6.788032189014539,"dropZones":["0","1","2","3"],"type":{"library":"H5P.Image 1.1","params":{"contentName":"Bild","file":{"path":"images\/file-5ef9f825c9e80.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":757,"height":744},"alt":"Graph von f'"},"subContentId":"5e2f799e-abae-4872-a446-353f16f603f8","metadata":{"contentType":"Image","license":"U","title":"Unbenannt: Image","defaultLanguage":"de"}},"backgroundOpacity":100,"multiple":false},{"x":24.232633279483036,"y":51.61290322580645,"width":8.040051575121161,"height":6.788032189014539,"dropZones":["0","1","2","3"],"type":{"library":"H5P.Image 1.1","params":{"contentName":"Bild","file":{"path":"images\/file-5ef9f8312d5f9.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":736,"height":681},"alt":"Graph von f''"},"subContentId":"32afe5c8-5927-4b07-b1d6-39b8a0efd8e5","metadata":{"contentType":"Image","license":"U","title":"Unbenannt: Image","defaultLanguage":"de"}},"backgroundOpacity":100,"multiple":false},{"x":1.615508885298869,"y":61.29032258064516,"width":7.414041882067851,"height":6.788032189014539,"dropZones":["0","1","2","3"],"type":{"library":"H5P.Image 1.1","params":{"contentName":"Bild","file":{"path":"images\/file-5ef9f8468f28d.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":747,"height":788},"alt":"Graph von f'''"},"subContentId":"c2c6b14c-073f-40f6-a760-356e89dc954b","metadata":{"contentType":"Image","license":"U","title":"Unbenannt: Image","defaultLanguage":"de"}},"backgroundOpacity":100,"multiple":false}],"dropZones":[{"x":0,"y":6.451612903225806,"width":9.390145395799676,"height":7.512116316639742,"correctElements":["0"],"showLabel":true,"backgroundOpacity":100,"tipsAndFeedback":{"tip":""},"single":false,"autoAlign":false,"label":"

Graph von f<\/div>\n"},{"x":27.463651050080774,"y":6.451612903225806,"width":8.764135702746366,"height":7.512116316639742,"correctElements":["1"],"showLabel":true,"backgroundOpacity":100,"tipsAndFeedback":{"tip":""},"single":false,"autoAlign":false,"label":"

Graph von f '<\/div>\n"},{"x":51.69628432956381,"y":6.451612903225806,"width":8.764135702746366,"height":7.512116316639742,"correctElements":["2"],"showLabel":true,"backgroundOpacity":100,"tipsAndFeedback":{"tip":""},"single":false,"autoAlign":false,"label":"

Graph von f ''<\/div>\n"},{"x":77.38287560581583,"y":6.451612903225806,"width":8.764135702746366,"height":7.512116316639742,"correctElements":["3"],"showLabel":true,"backgroundOpacity":100,"tipsAndFeedback":{"tip":""},"single":false,"autoAlign":false,"label":"

Graph von f '''<\/div>\n"}]}},"overallFeedback":[{"from":0,"to":100}],"behaviour":{"enableRetry":false,"enableCheckButton":true,"showSolutionsRequiresInput":true,"singlePoint":false,"applyPenalties":true,"enableScoreExplanation":true,"dropZoneHighlighting":"dragging","autoAlignSpacing":2,"enableFullScreen":false,"showScorePoints":true,"showTitle":true},"grabbablePrefix":"Ziehbares Element {num} von {total}.","grabbableSuffix":"Abgelegt in Ablagezone {num}.","dropzonePrefix":"Ablagezone {num} von {total}.","noDropzone":"Keine Ablagezone.","tipLabel":"Hinweis zeigen","tipAvailable":"Hinweis verf\u00fcgbar","correctAnswer":"Richtige Antwort","wrongAnswer":"Falsche Antwort","feedbackHeader":"R\u00fcckmeldung","scoreBarLabel":"Du hast :num von :total Punkten erreicht.","scoreExplanationButtonLabel":"Zeige Erkl\u00e4rung der Punktevergabe","localize":{"fullscreen":"Vollbild","exitFullscreen":"Vollbild beenden"},"a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Eingaben werden als richtig, falsch oder unbeantwortet markiert.","a11yRetry":"Die Aufgabe wiederholen. Alle Versuche werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet."},"library":"H5P.DragQuestion 1.13","metadata":{"contentType":"Drag and Drop","license":"U","title":"Ordne die Graphen der Funktion f, f ',f '' und f ''' zu.","defaultLanguage":"de"},"subContentId":"66febace-894d-4555-8bbe-93543691c18e"},{"params":{"media":{"disableImageZooming":false},"text":"

Bestimme die Gleichung der Tangente an den Graphen der Funktion f im Punkt P.<\/p>\n","overallFeedback":[{"from":0,"to":100}],"showSolutions":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","checkAnswer":"\u00dcberpr\u00fcfen","notFilledOut":"Bitte f\u00fclle alle L\u00fccken aus, um die L\u00f6sung ansehen zu k\u00f6nnen","answerIsCorrect":"':ans' ist korrekt","answerIsWrong":"':ans' ist falsch","answeredCorrectly":"Korrekt beantwortet","answeredIncorrectly":"Falsch beantwortet","solutionLabel":"Korrekte Antwort:","inputLabel":"L\u00fccke @num von @total","inputHasTipLabel":"Tipp verf\u00fcgbar","tipLabel":"Tipp","behaviour":{"enableRetry":false,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":true},"scoreBarLabel":"Du hast :num von :total Punkten erreicht.","confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"questions":["

a) \\( f(x) = x\u00b2 - 3 \\) \\( P( 1 | -2) \\)<\/p>\n\n

Tangentengleichung t : y = *2* x + * -4*<\/p>\n\n

a) \\( f(x) = \\frac{1}{x} \\) \\( P( 2 | \\frac{1}{2}) \\)<\/p>\n\n

Tangentengleichung t : y = *-0,25\/-0.25* x + *1\/+1*<\/p>\n\n

<\/p>\n\n

<\/p>\n"],"a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Eingaben werden als richtig, falsch oder unbeantwortet markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtigen L\u00f6sungen werden in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Eingaben werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet.","a11yCheckingModeHeader":"\u00dcberpr\u00fcfen-Modus aktiv"},"library":"H5P.Blanks 1.12","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"Bestimme die Tangente","defaultLanguage":"de"},"subContentId":"531fdb9f-03ca-42f9-8e11-251093b93c3e"},{"params":{"media":{"type":{"params":{"contentName":"Bild","file":{"path":"images\/file-5ef8898ff1eb7.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":937,"height":477}},"library":"H5P.Image 1.1","metadata":{"contentType":"Image","license":"CC0 1.0","title":"Unbenannt: Image","authors":[{"name":"heidenreich","role":"Author"}],"source":"https:\/\/pixabay.com\/de\/photos\/hei%C3%9Fluftballon-ballonfahren-ballon-1245927\/","defaultLanguage":"de"},"subContentId":"81ea9bc2-885b-4d73-8feb-014d4ad10256"},"disableImageZooming":false},"answers":[{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

Die Ballonfahrt dauerte etwa 4,5 Stunden.<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

Die gr\u00f6\u00dfte \u00c4nderung der Steiggeschwindigkeit war knapp 3 Stunden nach dem Start.<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

Die gr\u00f6\u00dfte \u00c4nderung der Steiggeschwindigkeit war etwa 1,5 Stunden nach dem Start.<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

Zwei Stunden nach dem Start betrug die momentane Steiggeschwinidigkeit etwa 0,3 \\( \\frac{km}{h} \\).<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

In den ersten beiden Stunden nach dem Start betrug die durchschnittliche Steiggeschwindigkeit etwa 0,3 \\( \\frac{km}{h} \\).<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

Die Sinkgeschwindigkeit nahm bis zur Landung immer mehr zu.<\/div>\n"}],"overallFeedback":[{"from":0,"to":100}],"behaviour":{"enableRetry":false,"enableSolutionsButton":true,"enableCheckButton":true,"type":"auto","singlePoint":false,"randomAnswers":false,"showSolutionsRequiresInput":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false,"passPercentage":100,"showScorePoints":true},"UI":{"checkAnswerButton":"\u00dcberpr\u00fcfen","showSolutionButton":"L\u00f6sung anzeigen","tryAgainButton":"Wiederholen","tipsLabel":"Hinweis anzeigen","scoreBarLabel":"Du hast :num von :total Punkten erreicht.","tipAvailable":"Hinweis verf\u00fcgbar","feedbackAvailable":"R\u00fcckmeldung verf\u00fcgbar","readFeedback":"R\u00fcckmeldung vorlesen","wrongAnswer":"Falsche Antwort","correctAnswer":"Richtige Antwort","shouldCheck":"H\u00e4tte gew\u00e4hlt werden m\u00fcssen","shouldNotCheck":"H\u00e4tte nicht gew\u00e4hlt werden sollen","noInput":"Bitte antworte, bevor du die L\u00f6sung ansiehst","a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Auswahlen werden als richtig, falsch oder fehlend markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtigen L\u00f6sungen werden in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Versuche werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet."},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"

Ein Hei\u00dfluftballon steigt senkrecht in die H\u00f6he. Die Funktion h mit h(t) = 0.05t\u00b3 + 0.2t\u00b2 + 0.1t gibt die H\u00f6he in km ab dem Start (t = 0, t in Stunden) an. Abgebildet ist der Graph von h.<\/p>\n\n

Kreuze die wahren Aussagen an.<\/p>\n"},"library":"H5P.MultiChoice 1.14","metadata":{"contentType":"Multiple Choice","license":"U","title":"Ballonfahrt","defaultLanguage":"de"},"subContentId":"590e1303-fcdc-4f27-95b9-80de38825611"}],"disableBackwardsNavigation":false,"randomQuestions":true,"endGame":{"showResultPage":true,"showSolutionButton":true,"noResultMessage":"Dein Ergebnis:","message":"Du hast @score Punkte von @total m\u00f6glichen.","overallFeedback":[{"from":0,"to":45,"feedback":"Leider hast du das Thema noch nicht ausreichend verstanden. Du musst dir die Inhalte zum Thema nochmal genauer anschauen."},{"from":46,"to":60,"feedback":"Du hast das Thema in den Grundz\u00fcgen verstanden. Du musst dir einzelne Inhalte zum Thema nochmal genauer anschauen."},{"from":61,"to":75,"feedback":"Gut! Du hast das Thema verstanden. Wenige Inhalte zum Thema musst du dir nochmal genauer anschauen."},{"from":76,"to":90,"feedback":"Prima! Du hast das Thema gut verstanden. Deinem weiteren Lernfortschritt steht nichts im Weg!"},{"from":91,"to":100,"feedback":"Hervorragend! Du hast das Thema sehr gut verstanden und durchdrungen."}],"solutionButtonText":"L\u00f6sung anzeigen","retryButtonText":"Wiederholen","finishButtonText":"Beenden","showAnimations":false,"skippable":false,"skipButtonText":"Skip video","showRetryButton":true},"override":{"checkButton":true},"texts":{"prevButton":"Zur\u00fcck","nextButton":"Weiter","finishButton":"Beenden","textualProgress":"Aktuelle Frage: @current von @total Fragen","jumpToQuestion":"Frage %d von %total","questionLabel":"Frage","readSpeakerProgress":"Frage @current von @total","unansweredText":"Unbeantwortet","answeredText":"Beantwortet","currentQuestionText":"Aktuelle Frage"}}

Ableitung: Differenzenquotient, Änderungsrate