CK12 Calculus - Single Variable

when. We note that since Hencewe

havea minimumsurfacearea when and.
LessonSummary

1. We usedthe First and SecondDerivativeTests to find absolutemaximumand minimumvaluesof a
   function.


2. We usedthe First and SecondDerivativeTests to solveoptimizationapplications.
   ReviewQuestions
   In problems#1–4,find the absolutemaximumand absoluteminimumvalues,if they exist.


3. on


4. on


5. on


6. on


7. Find the dimensionsof a rectanglehavingarea whoseperimeteris as smallas possible.


8. Find two numberswhoseproductis and whosesum is a minimum.


9. Johnis shootinga basketballfrom half-court.It is approximately ft from the half courtline to the hoop.
   The function modelsthe basketball’s heightabovethe ground in feet,
   whenit is feet from the hoop.How manyfeet from Johnwill the ball reachits highestheight?Whatis that
   height?


10. The heightof a modelrocket secondsinto flight is givenby the formula
    .
    a. How long will it take for the rocketto attainits maximumheight?
    b. Whatis the maximumheightthat the rocketwill reach?
    c. How long will the flightlast?


11. Showthat of all rectanglesof a givenperimeter, the rectanglewith the greatestarea is a square.