{"interactiveVideo":{"video":{"startScreenOptions":{"title":"Optimization part I","hideStartTitle":false,"shortStartDescription":"this is the 1st part of sample optimization topic"},"textTracks":{"videoTrack":[{"label":"Subtitles","kind":"subtitles","srcLang":"en"}]},"files":[{"path":"https:\/\/youtu.be\/JNeuEuK4AkA","mime":"video\/YouTube","copyright":{"license":"U"}}]},"assets":{"interactions":[{"x":48.458149779735685,"y":50.88062622309197,"width":10,"height":10,"duration":{"from":20.469,"to":24.469},"libraryTitle":"True\/False Question","action":{"library":"H5P.TrueFalse 1.8","params":{"media":{"disableImageZooming":false},"correct":"false","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false,"feedbackOnWrong":"This function has to be continuous: EVT requires a continuous function in order for it to achieve absolute max and absolute min."},"l10n":{"trueText":"True","falseText":"False","score":"You got @score of @total points","checkAnswer":"Check","showSolutionButton":"Show solution","tryAgain":"Retry","wrongAnswerMessage":"Wrong answer","correctAnswerMessage":"Correct answer","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"},"question":"

If a function \\(f\\) is defined on a closed interval \\([a,b]\\), then \\(f\\) attains an absolute maximum value \\(f(c)\\) and an absolute minimum value \\(f(d)\\) at some numbers \\(c\\) and \\(d\\) in \\([a,b]\\). <\/p>\n"},"subContentId":"9e7e76e0-c00e-4cb7-beac-6308a54efd6d","metadata":{"contentType":"True\/False Question","license":"U","title":"True\/False Question: Extreme Value Theorem"}},"pause":true,"displayType":"button","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""},"requireCompletion":false},"label":"

EVT<\/p>\n"},{"x":42.951541850220266,"y":60.665362035225044,"width":10,"height":10,"duration":{"from":145.24,"to":150.24},"libraryTitle":"Multiple Choice","action":{"library":"H5P.MultiChoice 1.16","params":{"media":{"disableImageZooming":false},"answers":[{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

The area always increases.<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

The area will first increase then decrease.<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

The area will eventaully become 0 again.<\/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":"

Can you guess once the width of the rectagle gets shorter than \\(\\frac{1}{2}\\)m, and the height of the rectangle gets taller than 0, what happens to the area of the rectangle?<\/p>\n"},"subContentId":"9c8647cd-8f4c-40f8-88af-9dd0f9b152b3","metadata":{"contentType":"Multiple Choice","license":"U","title":"How would the area of the rectangle change?"}},"pause":true,"displayType":"button","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""},"requireCompletion":false},"label":"

MCQ<\/p>\n"},{"x":47.797356828193834,"y":46.08610567514677,"width":10,"height":10,"duration":{"from":274.68,"to":280.68},"libraryTitle":"Multiple Choice","action":{"library":"H5P.MultiChoice 1.16","params":{"media":{"disableImageZooming":false},"answers":[{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

\\(x(\\frac{1}{2} -x)\\)<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

\\(y(\\frac{1}{2} -y)\\)<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

\\(\\frac{1}{2}x - x^2\\)<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

\\(\\frac{1}{2}y - y^2\\)<\/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":"

We can rewrite the function \\(s\\) as:<\/p>\n"},"subContentId":"6929fd54-2713-4458-950a-920535d80c73","metadata":{"contentType":"Multiple Choice","license":"U","title":"Choose the right option(s)."}},"pause":true,"displayType":"button","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""},"requireCompletion":false},"label":"

MCQ<\/p>\n"},{"x":47.797356828193834,"y":46.08610567514677,"width":10,"height":10,"duration":{"from":525.882,"to":528.882},"libraryTitle":"True\/False Question","action":{"library":"H5P.TrueFalse 1.8","params":{"media":{"disableImageZooming":false},"correct":"false","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false,"feedbackOnWrong":"Think about function such as \\(f(x) = x^3\\). At \\(x =0,\\) we have \\(f^\\prime (0) = 0\\) but the function doesn't have a maximum nor a minimum at \\(x =0.\\)"},"l10n":{"trueText":"True","falseText":"False","score":"You got @score of @total points","checkAnswer":"Check","showSolutionButton":"Show solution","tryAgain":"Retry","wrongAnswerMessage":"Wrong answer","correctAnswerMessage":"Correct answer","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"},"question":"

When \\(f^\\prime (c) =0\\), the function \\(f\\) has a maximum or minimum at \\(c\\).<\/p>\n"},"subContentId":"0e7f4785-b5d5-4b4c-a0ff-f59b514c53e2","metadata":{"contentType":"True\/False Question","license":"U","title":"True\/False Question"}},"pause":true,"displayType":"button","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""},"requireCompletion":false},"label":"

Fermat's Theorem<\/p>\n"},{"x":47.797356828193834,"y":46.08610567514677,"width":10,"height":10,"duration":{"from":573.63,"to":576.63},"libraryTitle":"Drag Text","action":{"library":"H5P.DragText 1.10","params":{"taskDescription":"Drag the words into the correct boxes","overallFeedback":[{"from":0,"to":100}],"checkAnswer":"Check","tryAgain":"Retry","showSolution":"Show solution","dropZoneIndex":"Drop Zone @index.","empty":"Drop Zone @index is empty.","contains":"Drop Zone @index contains draggable @draggable.","ariaDraggableIndex":"@index of @count draggables.","tipLabel":"Show tip","correctText":"Correct!","incorrectText":"Incorrect!","resetDropTitle":"Reset drop","resetDropDescription":"Are you sure you want to reset this drop zone?","grabbed":"Draggable is grabbed.","cancelledDragging":"Cancelled dragging.","correctAnswer":"Correct answer:","feedbackHeader":"Feedback","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"instantFeedback":false},"scoreBarLabel":"You got :num out of :total points","textField":"Suppose \\(f^{\\prime \\prime}\\) is continuous near \\(c\\). \nIf \\(f^\\prime (c) = 0\\) and \\(f^{\\prime \\prime}(c) >0,\\) then \\(f\\) has a *local minimum* at \\(c\\). If \\(f^\\prime (c) = 0\\) and \\(f^{\\prime \\prime}(c) <0,\\) then \\(f\\) has a *local maximum* at \\(c\\)."},"subContentId":"a76544f4-7652-46d3-bd64-f8e6802adf01","metadata":{"contentType":"Drag Text","license":"U","title":"Drag Text"}},"pause":true,"displayType":"button","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""},"requireCompletion":false},"label":"

The Second Derivative Test<\/p>\n"}],"endscreens":[{"time":626.781,"label":"10:26 Submit screen"},{"time":627,"label":"10:27 Submit screen"},{"time":678.436177,"label":"11:18 Submit screen"}]},"summary":{"task":{"library":"H5P.Summary 1.10","params":{"intro":"

What method did we use in this video to tell a local maximum from a local minimum point when we know \\(f^\\prime (c) =0\\)? <\/p>\n","summaries":[{"subContentId":"a4f19a14-b372-4d71-8fee-3f8d3467258e","tip":"","summary":["

The second derivative test.<\/p>\n","

Fermat's Theorem.<\/p>\n","

The first derivative test.<\/p>\n"]}],"overallFeedback":[{"from":0,"to":100}],"solvedLabel":"Progress:","scoreLabel":"Wrong answers:","resultLabel":"Your result","labelCorrect":"Correct.","labelIncorrect":"Incorrect! Please try again.","alternativeIncorrectLabel":"Incorrect","labelCorrectAnswers":"Correct answers.","tipButtonLabel":"Show tip","scoreBarLabel":"You got :num out of :total points","progressText":"Progress :num of :total"},"subContentId":"fdd1c5c4-4921-429c-b0dd-4234c28faf99","metadata":{"contentType":"Summary","license":"U","title":"Summary"}},"displayAt":4}},"override":{"autoplay":false,"loop":false,"showBookmarksmenuOnLoad":false,"showRewind10":false,"deactivateSound":false,"preventSkippingMode":"none"},"l10n":{"interaction":"Interaction","play":"Play","pause":"Pause","mute":"Mute","unmute":"Unmute","quality":"Video Quality","captions":"Captions","close":"Close","fullscreen":"Fullscreen","exitFullscreen":"Exit Fullscreen","summary":"Open summary dialog","bookmarks":"Bookmarks","endscreen":"Submit screen","defaultAdaptivitySeekLabel":"Continue","continueWithVideo":"Continue with video","playbackRate":"Playback Rate","rewind10":"Rewind 10 Seconds","navDisabled":"Navigation is disabled","sndDisabled":"Sound is disabled","requiresCompletionWarning":"You need to answer all the questions correctly before continuing.","back":"Back","hours":"Hours","minutes":"Minutes","seconds":"Seconds","currentTime":"Current time:","totalTime":"Total time:","singleInteractionAnnouncement":"Interaction appeared:","multipleInteractionsAnnouncement":"Multiple interactions appeared.","videoPausedAnnouncement":"Video is paused","content":"Content","answered":"@answered answered","endcardTitle":"@answered Question(s) answered","endcardInformation":"You have answered @answered questions, click below to submit your answers.","endcardInformationNoAnswers":"You have not answered any questions.","endcardInformationMustHaveAnswer":"You have to answer at least one question before you can submit your answers.","endcardSubmitButton":"Submit Answers","endcardSubmitMessage":"Your answers have been submitted!","endcardTableRowAnswered":"Answered questions","endcardTableRowScore":"Score","endcardAnsweredScore":"answered","endCardTableRowSummaryWithScore":"You got @score out of @total points for the @question that appeared after @minutes minutes and @seconds seconds.","endCardTableRowSummaryWithoutScore":"You have answered the @question that appeared after @minutes minutes and @seconds seconds."}}