Optimization Worksheet 3.6 With Answers - Calculus Maximus Page 10
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10Calculus Maximus
WS 3.6: Optimization
19. Find the positive number such that the sum of 6 times this number and 4 times its reciprocal is as small
as possible.
20. (Bonus Question) Calculator permitted: A storage bin is to be constructed by removing a sector with a
central angle,
, from a circular piece of tin of radius 5ft and folding the remainder of tin to form a
cone. What should
be in order to obtain a maximum volume of a storage bin formed in this
fashion? (Hint: Find an equation for Volume in terms of
in radians. Plot this function on a
reasonable window and find the maximum numerically.) Box your final Volume equation as a
function of
, write down your graphing window (x and y), and give your final answer in radians and
degrees to three decimal places. Did you get the same answer as Farmer Leibniz? If not, start over,
this time more correctly. You will need the arc length, s, formula: s r ,
where
is in radians.
Page 10 of 10
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