{"scoreShow":"Show score","tryAgain":"Retry","question":{"settings":{"size":{"width":1200,"height":900},"background":{"path":"images\/background-5f16d725efcd1.png","mime":"image\/png","copyright":{"license":"CC BY-SA","title":"notwendige Bedingung Extrema","author":"Hunor Karsa","year":"2020","version":"4.0","source":"https:\/\/apps.zum.de\/apps\/notwendige-bedingung-fuer-innere-extremstellen-lueckenbeweis"},"width":2566,"height":2132}},"task":{"elements":[{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

f'(x0<\/span>) = 0<\/p>\n"},"subContentId":"0c87e2a4-eb41-439f-8e1b-a84daac6221e","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"x":1.1410314925002,"y":3.0422878005363,"width":4.2095237629754,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

f(x0<\/span>)<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"9b49fd75-3846-48d9-b095-162f7a44a04f"},"x":1.1410314925002,"y":16.732582902949,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

f(x0<\/span>)<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"b89f8324-b07f-48d4-96df-defdaa20411d"},"x":5.7051574625012,"y":16.732582902949,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

f(x)<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"ff3ca598-1774-4d2c-aa8f-519b9cc63e02"},"x":1.1410314925002,"y":12.169151202145,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

f(x)<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"f3b04b74-7d26-4dff-94c1-3fafca0e235b"},"x":5.7051574625012,"y":12.169151202145,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

= f'(x0<\/span>)<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"d07f8453-a7e1-412c-b036-1b4f263f8ad2"},"x":1.1410314925002,"y":7.6057195013406,"width":3.4952380486897,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

x0<\/span><\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"eeaccdae-bda4-4ee7-a820-aea2395dd9fd"},"x":5.7051574625012,"y":25.859446304558,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

x0<\/span><\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"bd92ed9e-ea71-4887-bce7-166858caec18"},"x":1.1410314925002,"y":25.859446304558,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

x<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"b35bf690-e975-411f-83b4-1ace6e773d95"},"x":1.1410314925002,"y":21.296014603754,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

x<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"c2c3c8e9-599b-4b9d-849b-516be6f5ed1a"},"x":5.7051574625012,"y":21.296014603754,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

\u2264<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"af76bceb-72d8-4732-9ef0-332ca2ad6985"},"x":1.1410314925002,"y":34.986309706167,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

\u2264<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"fca0f219-2147-457c-a962-58603e014e4f"},"x":5.7051574625012,"y":34.986309706167,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

\u2265<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"9d76c88d-10e6-4973-9586-7bc269f7cea6"},"x":1.1410314925002,"y":39.549741406971,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

\u2265<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"cd80c894-673a-42e4-bdda-b1f0ee3ea14e"},"x":5.7051574625012,"y":39.549741406971,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

\u2264<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"5d067cab-e11f-4633-aac6-0530ea8356e3"},"x":10.269283432502,"y":34.986309706167,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

><\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"b34edc28-e778-49b1-a479-8eed0d95be23"},"x":1.1410314925002,"y":44.113173107776,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

=<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"d3ae125d-89ae-41be-8b55-e259216fbeb5"},"x":1.1410314925002,"y":30.422878005363,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false},{"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

=<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"f340fcf2-2c41-44c8-a5c7-bd2ce986ae01"},"x":5.7051574625012,"y":30.422878005363,"width":2.0666666201183,"height":1.2095237629754,"dropZones":["0","1","2","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17"],"backgroundOpacity":100,"multiple":false}],"dropZones":[{"x":81.05022831050229,"y":3.0441400304414,"width":8.561643835616438,"height":2.0547945205479454,"correctElements":["0"],"showLabel":false,"backgroundOpacity":0,"label":"

Ziel<\/div>\n","single":false,"autoAlign":true,"tipsAndFeedback":{"tip":"","feedbackOnCorrect":"","feedbackOnIncorrect":""}},{"x":28.881278538812786,"y":20.85235920852359,"width":2.5785721881049,"height":2.0571428571429,"correctElements":["3","4"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

f(x) oben<\/div>\n"},{"x":28.19634703196347,"y":35.920852359208524,"width":3.4246575342465753,"height":2.0547945205479454,"correctElements":["3","4"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

f(x) unten<\/div>\n"},{"x":34.24657534246575,"y":35.920852359208524,"width":3.4246575342465753,"height":2.0547945205479454,"correctElements":["1","2"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

f(xo) unten<\/div>\n"},{"x":31.506849315068493,"y":56.3165905631659,"width":2.5785721881049,"height":2.0571428571429,"correctElements":["8","9"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

x links<\/div>\n"},{"x":37.21461187214612,"y":56.3165905631659,"width":2.5785721881049,"height":2.0571428571429,"correctElements":["6","7"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

xo links<\/div>\n"},{"x":75.79908675799086,"y":56.3165905631659,"width":2.5785721881049,"height":2.0571428571429,"correctElements":["8","9"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

x rechts<\/div>\n"},{"x":81.39269406392694,"y":56.3165905631659,"width":2.5785721881049,"height":2.0571428571429,"correctElements":["6","7"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

xo rechts<\/div>\n"},{"x":34.24657534246575,"y":63.926940639269404,"width":2.5785721881049,"height":2.0571428571429,"correctElements":["13","12"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

\u2265 mitte links<\/div>\n"},{"x":88.81278538812785,"y":59.665144596651444,"width":2.5785721881049,"height":2.0571428571429,"correctElements":["10","11","14"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

\u2264 rechts oben<\/div>\n"},{"x":84.47488584474885,"y":63.926940639269404,"width":2.5785721881049,"height":2.0571428571429,"correctElements":["10","11","14"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

\u2264 rechts unten<\/div>\n"},{"x":79.337899543379,"y":71.99391171993912,"width":2.5785721881049,"height":2.0571428571429,"correctElements":["15"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

><\/div>\n"},{"x":52.62557077625571,"y":78.69101978691019,"width":2.5785721881049,"height":2.0571428571429,"correctElements":["16","17"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

= oben<\/div>\n"},{"x":40.41095890410959,"y":87.51902587519025,"width":2.5785721881049,"height":2.0571428571429,"correctElements":["12","13"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

\u2265 unten<\/div>\n"},{"x":57.077625570776256,"y":87.36681887366818,"width":2.5785721881049,"height":2.0571428571429,"correctElements":["10","11","14"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

\u2264 unten<\/div>\n"},{"x":50,"y":93.91171993911719,"width":2.5785721881049,"height":2.0571428571429,"correctElements":["16","17"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

=<\/div>\n"},{"x":57.534246575342465,"y":93.91171993911719,"width":4.280821917808219,"height":2.0547945205479454,"correctElements":["5"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

=f'(x0)<\/div>\n"},{"x":37.32876712328767,"y":21.00456621004566,"width":2.5785721881049,"height":2.0571428571429,"correctElements":["2","1"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

f(x0) oben<\/div>\n"}]}},"behaviour":{"enableRetry":true,"singlePoint":false,"showSolutionsRequiresInput":true,"enableScoreExplanation":true,"applyPenalties":true,"dropZoneHighlighting":"dragging","autoAlignSpacing":2,"enableFullScreen":true,"showScorePoints":true,"enableCheckButton":true,"showTitle":true},"scoreExplanation":"Correct answers give +1 point. Incorrect answers give -1 point. The lowest possible score is 0.","localize":{"fullscreen":"Fullscreen","exitFullscreen":"Exit fullscreen"},"overallFeedback":[{"from":0,"to":100,"feedback":"You got @score of @total points."}],"grabbablePrefix":"Grabbable {num} of {total}.","grabbableSuffix":"Placed in dropzone {num}.","dropzonePrefix":"Dropzone {num} of {total}.","noDropzone":"No dropzone.","tipLabel":"Show tip.","tipAvailable":"Tip available","correctAnswer":"Correct answer","wrongAnswer":"Wrong answer","feedbackHeader":"Feedback","scoreBarLabel":"You got :num out of :total points","scoreExplanationButtonLabel":"Show score explanation"}

f'

Notwendige Bedingung für innere Extremstellen - Lückenbeweis