CK12 Calculus - Single Variable

10. Showthat of all rectanglesof a givenarea,the rectanglewith the smallestperimeteris a square.

Answers

1. 
   

   Absoluteminimumat. Absolutemaximumat

   
   


2. 
   

   Absoluteminimumat Absolutemaximumat

   
   


3. 
   

   Absoluteminimumat Absolutemaximumat

   
   


4. 
   

   Absoluteminimumat Absolutemaximumat

   
   


5. 
   


6. 
   


7. 
   

   At ft, the basketballwill reacha heightof ft.

   
   


8. 
   

   The rocketwill take approximately sec to attainits maximumheightof ft.; the rocketwill
   hit the groundat sec.

   
   

ApproximationErrors

LearningObjectives
A studentwill be able to:

• Extendthe MeanValue Theoremto makelinearapproximations.


• Analyzeerrorsin linearapproximations.


• Extendthe MeanValue Theoremto makequadraticapproximations.


• Analyzeerrorsin quadraticapproximations.
  Introduction
  In this lessonwe will use the MeanValue Theoremto makeapproximationsof functions.We will applythe
  Theoremdirectlyto makelinearapproximationsand then extendthe Theoremto makequadraticapproxi-
  mationsof functions.

Let’s considerthe tangentline to the graphof a function at the point The equationof this line
is We observefromthe graphthat as we consider near the valueof
is very closeto