{"l10n":{"slide":"Slide","yourScore":"Your Score","maxScore":"Max Score","showSolutions":"Show solutions","exportAnswers":"Export text","hideKeywords":"Hide keywords list","showKeywords":"Show keywords list","fullscreen":"fullscreen","exitFullscreen":"Exit fullscreen","prevSlide":"Previous slide","nextSlide":"Next slide","currentSlide":"Current slide","lastSlide":"Last slide","solutionModeTitle":"Exit solution mode","solutionModeText":"Solution Mode","summaryMultipleTaskText":"Text when multiple tasks on a page","scoreMessage":"You achieved:","shareFacebook":"Share on Facebook","shareTwitter":"Share on Twitter","retry":"Retry","summary":"Summary","solutionsButtonTitle":"Show comments","printTitle":"Print","printIngress":"How would you like to print this presentation?","printAllSlides":"Print all slides","printCurrentSlide":"Print current slide","total":"TOTAL","shareGoogle":"Share on Google+","noTitle":"No title","accessibilitySlideNavigationExplanation":"Use left and right arrow to change slide in that direction whenever canvas is selected.","accessibilityCanvasLabel":"Presentation canvas. Use left and right arrow to move between slides.","containsNotCompleted":"@slideName contains not completed interaction","containsCompleted":"@slideName contains completed interaction","slideCount":"Slide @index of @total","containsOnlyCorrect":"@slideName only has correct answers","containsIncorrectAnswers":"@slideName has incorrect answers","score":"Score","totalScore":"Total Score","shareResult":"Share Result","accessibilityTotalScore":"You got @score of @maxScore points in total","accessibilityEnteredFullscreen":"Entered fullscreen","accessibilityExitedFullscreen":"Exited fullscreen"},"override":{"hideSummarySlide":false,"activeSurface":false,"showSolutionButton":"on","retryButton":"on","enablePrintButton":true,"social":{"showFacebookShare":true,"facebookShare":{"url":"@currentpageurl","quote":"I scored @percentage on a task at @currentpageurl."},"showTwitterShare":false,"twitterShare":{"statement":"I scored @percentage on a task at @currentpageurl.","url":"@currentpageurl","hashtags":"h5p, course"},"showGoogleShare":false,"googleShareUrl":"@currentpageurl"},"summarySlideSolutionButton":true,"summarySlideRetryButton":true},"presentation":{"slides":[{"elements":[{"x":74.074074074074,"y":86.881720430108,"width":23.9651416122,"height":7.3118279569892,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"

zum Monotonie-Aufschrieb<\/span><\/p>\n"},"subContentId":"56389ab2-a70f-4265-9099-d28023126dd8","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"alwaysDisplayComments":false,"backgroundOpacity":50,"displayAsButton":false,"invisible":false,"solution":"","buttonSize":"big","goToSlideType":"specified"},{"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Extrempunkte und die zweite Ableitung<\/strong><\/h2>\n\n
Um diese soll es heute genauer gehen! Als Grundlage daf\u00fcr brauchst du die Monotonie:<\/p>\n\n
1. Lies dir in deinem Aufschrieb nochmals den Abschnitt zur Monotonie genau durch!<\/p>\n\n
Danach geht es weiter mit der n\u00e4chsten Folie (unten auf den Pfeil nach rechts klicken).<\/p>\n"},"subContentId":"2a8c73bd-0a24-4896-915f-d552d7c40f52","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"x":2.1786492374728,"y":4.2818266345609,"width":46.949891067538,"height":60.215053763441,"alwaysDisplayComments":false,"backgroundOpacity":70,"displayAsButton":false,"solution":"","invisible":false,"buttonSize":"big","goToSlideType":"specified"},{"x":74.15485278080698,"y":47.41379310344828,"width":24.074814253574,"height":40,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","file":{"path":"images\/file-5ebe8695d576c.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":1838,"height":1546},"alt":"NSW F14"},"subContentId":"bed6aceb-cbe7-4cf6-8a6d-987c5fb9b355","metadata":{"contentType":"Image","license":"CC BY-SA","title":"Monotonie-Aufschrieb","authors":[{"name":"Hunor Karsa","role":"Author"}],"licenseVersion":"4.0","source":"https:\/\/apps.zum.de\/apps\/f-kriterium-fuer-innere-extremstellen"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":74.15485278080698,"y":47.41379310344828,"width":23.9651416122,"height":47.311827956989,"goToSlide":11,"backgroundOpacity":0,"displayAsButton":false,"invisible":false,"title":"Springe zum Aufschrieb","buttonSize":"big","goToSlideType":"specified"}],"slideBackgroundSelector":{}},{"elements":[{"x":22.872004357298476,"y":4.317823275862069,"width":54.46623093681917,"height":90.51724137931035,"action":{"library":"H5P.MultiChoice 1.14","params":{"media":{"disableImageZooming":false},"answers":[{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"
Wenn f'(x) > 0 ist, dann ist f streng monoton fallend.<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"
Wenn f streng monoton fallend ist, dann ist f'(x) negativ.<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"
Wenn f' positiv ist, dann ist f streng monoton steigend.<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"
Wenn der Graph von f die ganze Zeit f\u00e4llt, dann ist f' negativ oder Null.<\/div>\n"}],"overallFeedback":[{"from":0,"to":100}],"behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"type":"auto","singlePoint":false,"randomAnswers":true,"showSolutionsRequiresInput":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false,"passPercentage":100,"showScorePoints":true},"UI":{"checkAnswerButton":"Check","showSolutionButton":"Show solution","tryAgainButton":"Retry","tipsLabel":"Show tip","scoreBarLabel":"You got :num out of :total points","tipAvailable":"Tip available","feedbackAvailable":"Feedback available","readFeedback":"Read feedback","wrongAnswer":"Wrong answer","correctAnswer":"Correct answer","shouldCheck":"Should have been checked","shouldNotCheck":"Should not have been checked","noInput":"Please answer before viewing the solution"},"confirmCheck":{"header":"Finish ?","body":"Are you sure you wish to finish ?","cancelLabel":"Cancel","confirmLabel":"Finish"},"confirmRetry":{"header":"Retry ?","body":"Are you sure you wish to retry ?","cancelLabel":"Cancel","confirmLabel":"Confirm"},"question":"
Markiere alle korrekten Aussagen!<\/p>\n"},"subContentId":"6654588c-0682-4086-9076-3c4ccd2a5c6f","metadata":{"contentType":"Multiple Choice","license":"U","title":"Untitled Multiple Choice"}},"alwaysDisplayComments":false,"backgroundOpacity":70,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}],"slideBackgroundSelector":{}},{"elements":[{"action":{"library":"H5P.Blanks 1.12","params":{"questions":["
Meistens kann man eine Funktion auch mehrfach ableiten:<\/p>\n\n
f(x) = x^2<\/p>\n\n
f'(x) = 2x\/2 x<\/p>\n\n
f''(x) = 2<\/p>\n","
Das ist zwar sch\u00f6n, aber wof\u00fcr ist das gut?<\/p>\n"],"showSolutions":"Show solutions","tryAgain":"Retry","checkAnswer":"Check","notFilledOut":"Please fill in all blanks","text":"
F\u00fclle die L\u00fccken!<\/p>\n","behaviour":{"enableSolutionsButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"enableRetry":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false,"enableCheckButton":true},"answerIsCorrect":"':ans' is correct","answerIsWrong":"':ans' is wrong","answeredCorrectly":"Answered correctly","answeredIncorrectly":"Answered incorrectly","solutionLabel":"Correct answer:","inputLabel":"Blank input @num of @total","inputHasTipLabel":"Tip available","tipLabel":"Tip","confirmCheck":{"header":"Finish ?","body":"Are you sure you wish to finish ?","cancelLabel":"Cancel","confirmLabel":"Finish"},"confirmRetry":{"header":"Retry ?","body":"Are you sure you wish to retry ?","cancelLabel":"Cancel","confirmLabel":"Confirm"},"overallFeedback":[{"from":0,"to":100,"feedback":"You got @score of @total blanks correct."}],"scoreBarLabel":"You got :num out of :total points","media":{"disableImageZooming":false}},"subContentId":"a648de70-c1fd-4692-9261-ce44bc0a9204","metadata":{"title":"f'' Bedeutung","license":"U","contentType":"Fill in the Blanks"}},"x":2.171089324618736,"y":4.3253017241379315,"width":53.37690631808279,"height":79.74137931034484,"alwaysDisplayComments":false,"backgroundOpacity":70,"displayAsButton":false,"solution":"","invisible":false,"buttonSize":"big","goToSlideType":"specified"},{"action":{"library":"H5P.Blanks 1.12","params":{"questions":["
(Achte auf korrekte Rechtschreibung - z. B. Gro\u00df- und Kleinschreibung!)<\/p>\n\n
Die zweite Ableitung f'' ist die Ableitung von f'. Sie gibt also die Steigung\/Steigung der Tangente\/Tangentensteigung\/momentane \u00c4nderung\/momentane \u00c4nderungsrate des Graphen von f' an - also alles genauso wie bisher, nur mit einem Strich mehr.<\/p>\n"],"showSolutions":"Show solutions","tryAgain":"Retry","checkAnswer":"Check","notFilledOut":"Please fill in all blanks","text":"
Probiere es mit einer Vermutung!<\/p>\n","behaviour":{"enableSolutionsButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"enableRetry":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false,"enableCheckButton":true},"answerIsCorrect":"':ans' is correct","answerIsWrong":"':ans' is wrong","answeredCorrectly":"Answered correctly","answeredIncorrectly":"Answered incorrectly","solutionLabel":"Correct answer:","inputLabel":"Blank input @num of @total","inputHasTipLabel":"Tip available","tipLabel":"Tip","confirmCheck":{"header":"Finish ?","body":"Are you sure you wish to finish ?","cancelLabel":"Cancel","confirmLabel":"Finish"},"confirmRetry":{"header":"Retry ?","body":"Are you sure you wish to retry ?","cancelLabel":"Cancel","confirmLabel":"Confirm"},"overallFeedback":[{"from":0,"to":100,"feedback":"You got @score of @total blanks correct."}],"scoreBarLabel":"You got :num out of :total points","media":{"disableImageZooming":false}},"metadata":{"title":"f'' Bedeutung","license":"U","contentType":"Fill in the Blanks"},"subContentId":"30f87dcb-8b85-4495-98bb-7507e8c8c517"},"x":58.82352941176471,"y":19.396551724137932,"width":39.21568627450981,"height":76.07758620689656,"alwaysDisplayComments":false,"backgroundOpacity":70,"displayAsButton":false,"solution":"","invisible":false,"buttonSize":"big","goToSlideType":"specified"}],"slideBackgroundSelector":{}},{"elements":[{"x":47.930283224401,"y":0,"width":38.344226579521,"height":100,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","file":{"path":"images\/file-5ebe8e3baa7de.png","mime":"image\/png","copyright":{"license":"U"},"width":1344,"height":1774},"alt":"3 Graphen"},"subContentId":"2dc3762b-9e9d-4afd-a366-bec031e7259e","metadata":{"contentType":"Image","license":"CC BY-SA","title":"zweimal ableiten","authors":[{"name":"Karsa","role":"Author"}],"licenseVersion":"4.0","source":"https:\/\/apps.zum.de\/apps\/f-kriterium-fuer-innere-extremstellen"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":2.1748692810457517,"y":6.480474137931035,"width":39.97821350762527,"height":34.48275862068966,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"
Gleich kommt der kniffligste Teil!<\/p>\n\n
Als Vorbereitung dazu:<\/p>\n\n
\u00dcbernimmt die Bilder rechts in dein \u00dcbungsheft und bearbeite die Aufgabe. Pr\u00fcfe danach mit der n\u00e4chsten Folie.<\/p>\n"},"subContentId":"5d3d5f3f-7b68-4c8d-a60a-6749eef9dda5","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"alwaysDisplayComments":false,"backgroundOpacity":70,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}],"slideBackgroundSelector":{}},{"slideBackgroundSelector":{},"elements":[{"x":3.271537622682661,"y":4.310344827586207,"width":63.18082788671024,"height":90.51724137931035,"action":{"library":"H5P.Video 1.5","params":{"visuals":{"fit":true,"controls":true},"playback":{"autoplay":false,"loop":false},"l10n":{"name":"Video","loading":"Video player loading...","noPlayers":"Found no video players that supports the given video format.","noSources":"Video is missing sources.","aborted":"Media playback has been aborted.","networkFailure":"Network failure.","cannotDecode":"Unable to decode media.","formatNotSupported":"Video format not supported.","mediaEncrypted":"Media encrypted.","unknownError":"Unknown error.","invalidYtId":"Invalid YouTube ID.","unknownYtId":"Unable to find video with the given YouTube ID.","restrictedYt":"The owner of this video does not allow it to be embedded."},"sources":[{"path":"videos\/sources-5ebe956eb2367.mp4","mime":"video\/mp4","copyright":{"license":"U"}}]},"subContentId":"c0348b89-2a50-497c-9825-6c0f6d6fa990","metadata":{"contentType":"Video","license":"CC BY-SA","title":"grafisch zweimal ableiten","authors":[{"name":"Hunor Karsa","role":"Author"}],"licenseVersion":"4.0","source":"https:\/\/apps.zum.de\/apps\/f-kriterium-fuer-innere-extremstellen"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":68.62745098039215,"y":64.65517241379311,"width":29.084967320261438,"height":30.172413793103452,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"
Kontrolliere deine L\u00f6sungen mit dem Film und dann bist du bereit f\u00fcr den ultimativen 2-seitigen Hirnschmalz-L\u00fcckentext! Den gibt es auf den n\u00e4chsten beiden Folien - yay!<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"64c88f6c-9ea7-450d-b0a9-75c5523ea66b"},"alwaysDisplayComments":false,"backgroundOpacity":70,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}]},{"slideBackgroundSelector":{},"elements":[{"x":0,"y":0,"width":100,"height":100,"action":{"library":"H5P.Blanks 1.12","params":{"media":{"disableImageZooming":false},"text":"
F\u00fclle die L\u00fccken und schau zur Hilfe in dein \u00dcbungsheft!<\/p>\n","overallFeedback":[{"from":0,"to":100}],"showSolutions":"Show solutions","tryAgain":"Retry","checkAnswer":"Check","notFilledOut":"Please fill in all blanks","answerIsCorrect":"':ans' is correct","answerIsWrong":"':ans' is wrong","answeredCorrectly":"Answered correctly","answeredIncorrectly":"Answered incorrectly","solutionLabel":"Correct answer:","inputLabel":"Blank input @num of @total","inputHasTipLabel":"Tip available","tipLabel":"Tip","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"You got :num out of :total points","confirmCheck":{"header":"Finish ?","body":"Are you sure you wish to finish ?","cancelLabel":"Cancel","confirmLabel":"Finish"},"confirmRetry":{"header":"Retry ?","body":"Are you sure you wish to retry ?","cancelLabel":"Cancel","confirmLabel":"Confirm"},"questions":["
Die Steigung der Tangente in einem Tiefpunkt ist gleich 0\/Null.<\/p>\n\n
Das hei\u00dft, f\u00fcr die Ableitung an der Stelle a gilt f \u2019(a) =0\/= 0\/ = 0.<\/p>\n\n
Da dies eine grunds\u00e4tzliche Voraussetzung f\u00fcr die Existenz eines Extrempunktes ist, spricht man von der notwendigen Bedingung, d.h.: nur die x-Werte, f\u00fcr die gilt f \u2019(x) =0\/= 0\/ = 0, kommen als x-Wert des Tiefpunktes in Betracht (Bewerber, Kandidaten).<\/p>\n\n
Die Nullstellen der ersten Ableitung m\u00fcssen nun n\u00e4her gepr\u00fcft (untersucht) werden. Vor Erreichen des Tiefpunktes f\u00e4llt\/sinkt das Schaubild der Funktion f, danach w\u00e4chst\/steigt es. <\/p>\n\n
F\u00fcr den Funktionswert der Ableitungsfunktion hei\u00dft das, kurz vor Erreichen von der Stelle a gilt: f'(x) <0\/< 0\/ < 0\/ist kleiner 0\/ist kleiner Null\/ist kleiner als 0\/ist kleiner als Null\/ist negativ und kurz nach \u201eVerlassen\u201c von a gilt: f'(x) >0\/> 0\/ > 0\/ist gr\u00f6\u00dfer 0\/ist gr\u00f6\u00dfer Null\/ist gr\u00f6\u00dfer als 0\/ist gr\u00f6\u00dfer als Null\/ist positiv. ...<\/p>\n"]},"subContentId":"6e5d8632-7ed6-44cf-acda-840f80cbef5c","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"Untitled Fill in the Blanks"}},"alwaysDisplayComments":false,"backgroundOpacity":70,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}]},{"slideBackgroundSelector":{},"elements":[{"x":0,"y":0,"width":100,"height":100,"action":{"library":"H5P.Blanks 1.12","params":{"media":{"disableImageZooming":false},"text":"
weiter geht's:<\/p>\n","overallFeedback":[{"from":0,"to":100}],"showSolutions":"Show solutions","tryAgain":"Retry","checkAnswer":"Check","notFilledOut":"Please fill in all blanks","answerIsCorrect":"':ans' is correct","answerIsWrong":"':ans' is wrong","answeredCorrectly":"Answered correctly","answeredIncorrectly":"Answered incorrectly","solutionLabel":"Correct answer:","inputLabel":"Blank input @num of @total","inputHasTipLabel":"Tip available","tipLabel":"Tip","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"You got :num out of :total points","confirmCheck":{"header":"Finish ?","body":"Are you sure you wish to finish ?","cancelLabel":"Cancel","confirmLabel":"Finish"},"confirmRetry":{"header":"Retry ?","body":"Are you sure you wish to retry ?","cancelLabel":"Cancel","confirmLabel":"Confirm"},"questions":["
Die y-Werte der Ableitungsfunktion gehen also an der Stelle a von negativen Werten \u00fcber zu positiven Werten. Das Schaubild der Ableitungsfunktion selbst steigt\/w\u00e4chst also. f' ist dort also streng monoton steigend\/wachsend. <\/p>\n\n
Der Wert der zweiten Ableitung zeigt mir bekannterweise immer den Wert der Tangentensteigung\/Steigung der Tangente\/Steigung\/momentanen \u00c4nderung\/momentanen \u00c4nderungsrate im Schaubild der ersten Ableitung. Wie wir aber bereits wissen, steigt\/w\u00e4chst das Schaubild der ersten Ableitung an der Stelle a.<\/p>\n\n
Wenn f''(a) also >\/gr\u00f6\u00dfer\/gr\u00f6\u00dfer als 0 ist, dann ist f' an seiner Nullstelle a streng monoton steigend. Dann muss f an der Stelle a einen Tiefpunkt besitzen.<\/p>\n\n
Genauso gilt: Wenn f'(b) = 0 ist und f''(b) < 0 ist, dann ist f' an der Stelle b streng monoton fallend\/monoton fallend\/fallend, hat also einen Vorzeichenwechsel von +\/Plus\/plus nach -\/\u2013\/Minus\/minus und an der Stelle b somit einen Hochpunkt. <\/p>\n"]},"subContentId":"6e5d8632-7ed6-44cf-acda-840f80cbef5c","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"Untitled Fill in the Blanks"}},"alwaysDisplayComments":false,"backgroundOpacity":70,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}]},{"slideBackgroundSelector":{},"elements":[{"x":1.0893246187363834,"y":2.1551724137931036,"width":23.965141612200437,"height":10.775862068965518,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"
\u00dcbernimm nun den Aufschrieb aus dem Film!<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"842f678f-3d19-4aad-8c4a-60fcf3fc9adb"},"alwaysDisplayComments":false,"backgroundOpacity":70,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":27.153762268266085,"y":0,"width":72.76688453159042,"height":100.00000000000001,"action":{"library":"H5P.Video 1.5","params":{"visuals":{"fit":true,"controls":true},"playback":{"autoplay":false,"loop":false},"l10n":{"name":"Video","loading":"Video player loading...","noPlayers":"Found no video players that supports the given video format.","noSources":"Video is missing sources.","aborted":"Media playback has been aborted.","networkFailure":"Network failure.","cannotDecode":"Unable to decode media.","formatNotSupported":"Video format not supported.","mediaEncrypted":"Media encrypted.","unknownError":"Unknown error.","invalidYtId":"Invalid YouTube ID.","unknownYtId":"Unable to find video with the given YouTube ID.","restrictedYt":"The owner of this video does not allow it to be embedded."},"sources":[{"path":"videos\/sources-5ebe9d3fbfe69.mp4","mime":"video\/mp4","copyright":{"license":"U"}}]},"subContentId":"3b4e718e-4efb-4320-ac81-7f0d0f676bf3","metadata":{"contentType":"Video","license":"CC BY-SA","title":"Folgerung aus der 2. Ableitung f\u00fcr Extrempunkte","authors":[{"name":"Hunor Karsa","role":"Author"}],"licenseVersion":"4.0","source":"https:\/\/apps.zum.de\/apps\/f-kriterium-fuer-innere-extremstellen"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}]},{"slideBackgroundSelector":{},"elements":[{"x":22.873965141612203,"y":0,"width":77.12418300653594,"height":100,"action":{"library":"H5P.DragQuestion 1.13","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":1263,"height":608},"background":{"path":"images\/background-5ebe9ed1d5f32.jpeg","mime":"image\/jpeg","copyright":{"license":"CC BY-SA","title":"Bsp. (ii)","author":"Hunor Karsa","year":"2020","version":"4.0","source":"https:\/\/apps.zum.de\/apps\/f-kriterium-fuer-innere-extremstellen"},"width":2527,"height":1216}},"task":{"elements":[{"x":74.19914855586643,"y":4.750358743529543,"width":3.7084459032534247,"height":1.9062198758561646,"dropZones":["0","1","2","3","4","5","6","7","8","9","10","11","12","13","14"],"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"
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Extrempunkt

f''-Kriterium für innere Extremstellen

Notwendige Bedingung für innere Extremstellen - Lückenbeweis