Section 4.3 – Optimization Problems
1. Find the point on the curve y 2 2x that is closest to the point (1, 4).
2. A cylindrical can is to have volume 1000cm3. Find the dimensions that would minimize the
amount of material used to make the can.
3. A man launches his boat from point A on the bank of a straight river 3km wide. He wants to
reach point B, 8km downstream on the opposite bank. If he can row 6km/hr and run 8km/hr,
where should he land his boat to reach B as quickly as possible?
4. A steel pipe is being carried down a hallway that is 9ft wide. At the end of the hallway is a right-
angled turn into a hallway that is 6ft wide. What is the longest pipe that can be carried
horizontally around this corner?