Probem35+Elana,+Susie



This problem involves minimizing the cost metal used to build a cylinder with a volume of Vcm³ And you are very smartly realizing that you need to work on the surface area -- so what are you trying to do: maximize it or minimize it? Make it clear!

V = V V= pi r²h h = V/pi r²

A = 2pi r² + 2pi rh A = 2pi r² + 2pi r(V/( pi r²) A = 2pi r² + 2(V/r)

take the derivative

A' = 4pi r - V/r²


 * not sure where to go because we do not have a number for VWould you know what to do if you //did// have a value for volume -- perhaps V = 100?? V = π? V = ʨ? these numbers are still just basically a symbol and don't change what you will do... so why not treat V as a number (constant)? The only uncomfortable part (for a moment) is that your answer will be in terms of V. The other uncomfortable part is that you will need to plug your answer into the original objective function, which will be a bit of a pain. You need to do this to justify that the behavior at the critical value will be greater (or less) than what is going on at the endpoints of the domain (and don't forget to do this also)