CK12 Calculus - Single Variable

d. For whatvaluesof do the tangentlines appearto havenegativeslope?

4. The cost of producing Hi-Fi stereoreceiversby Yamahaeachweekis modeledby the followingfunction:

a. Generatethe graphof usingyour calculator. (Hint:Changeyour viewingwindowto reflectthe high
values.)
b. For whatnumberof unitswill the functionbe maximized?

c. Estimatethe slopeof the tangentline at
d. Whereis marginalcost positive?

5. Find the area underthe curveof from to Use a rectanglemethodthat uses
   the minimumvalueof the functionwithinsub-intervals.Producethe approximationfor eachcaseof the
   subintervalcases.
   a. four sub-intervals.
   b. eightsub-intervals.
   c. Repeatpart a. usinga Mid-PointValue of the functionwithineachsub-interval.
   d. Whichof the answersin a.–c.providethe best estimateof the actualarea?


6. Considerthe function

a. Find the area underthe curvefrom to

b. Can you find the area underthe curvefrom to Why or why not? Whatis problematic
for this computation?

7. Find the areaunderthe curveof from to Use the Max Value rectangle
   methodwith six sub-intervalsto computethe area.


8. The Eiffel Toweris 320 metershigh.Supposethat you drop a ball off the top of the tower. The distance
   that it falls is a functionof time and is givenby

Find the velocityof the ball after seconds.(Hint:the averagevelocityfor a time intervalisaveragevelocity
= changein distance/changein time. Investigatethe averagevelocityfor intervalscloseto such
as and closerand see if a patternis evident.)

Answers

2. a. For