CK12 Calculus - Single Variable
everywherein .Hence isconcavedownin is not definedat , so is an absoluteminimum. Table Summary Analysis Domainand Range zerosat ...
on the interval GeneralProperties We note that is a continuousfunctionand thus attainsan absolutemaximumand minimumin Its domain ...
Intervalswheref is decreasing Relativeextrema relativemaximumat relativeminimumat absolutemaximumat absoluteminimumat , located ...
Differentiability Intervalswheref is increasing Intervalswheref is decreasing Relativeextrema Concavity Inflectionpoints Ana ...
Differentiability Intervalswheref is increasing Intervalswheref is decreasing Relativeextrema Concavity Inflectionpoints Ana ...
Intervalswheref is increasing Intervalswheref is decreasing Relativeextrema Concavity Inflectionpoints Answers Analysis Doma ...
2. Analysis Domainand Range zerosat -intercept at Interceptsand Zeros Asymptotesand limitsat infin-no asymptotes ity differentia ...
Asymptotesity and limitsat infin-HA differentiableat everypointof its domain Differentiability Intervalswheref is increasing Int ...
relativeminimumat located at the point Concavity concaveup in concavedownin Inflectionpoints locatedat the point Analysis Do ...
Differentiability differentiablein Intervalswheref is increasing Intervalswheref is decreasing relativeminimumat located at the ...
Optimization LearningObjectives A studentwill be able to: Use the First and SecondDerivativeTests to find absolutemaximumand mi ...
We first note that sincethis is a real-lifeapplication,we observethat both quantities, and are positiveor else the problemmakesn ...
We startedwith the generalvolumeformula , but quicklyrealizedthat we did not havesufficient informationto find sincewe had no in ...
Solution: The primaryequationis the functionthat modelsthe area of the pen and that we wish to maximize, The secondaryequationco ...
The feasibledomainof this functionis whichmakessensebecauseif is feet, then the figurewill be two -foot-longfencesgoingawayfrom ...
when. We note that since Hencewe havea minimumsurfacearea when and. LessonSummary We usedthe First and SecondDerivativeTests to ...
Showthat of all rectanglesof a givenarea,the rectanglewith the smallestperimeteris a square. Answers Absoluteminimumat. Abso ...
In otherwords,for valuescloseto the tangentline to the graphof a function at the point providesan approximationof or We call thi ...
for near Hence We observethat to approximate we needto evaluatethe linearapproximationat , and we have . If we wereto comparethi ...
In orderto view the differencesbetweenthe actualand approximatevalues,we can enterinto theY =menu the differencefunctionY 3 =Y 1 ...
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