Calculus Homework Help - Optimization Word Problem

markcus
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Calculus Homework Help -- Optimization Word Problem

I'm in a University Calculus class, and I am having trouble with one of my homework questions. Much help would be appreciated!

"Determine the height and radius of the cylinder of greatest volume that can be inscribed in a sphere of radius R units."

Also, we are learning about derivatives, so if the question is solved using them, please indicate!
Thank you so much!.
 
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welcome to pf!

hi markcus! welcome to pf! :wink:

show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 


hey i actually figured it out, i think i was just having trouble visualizing it, it's not that bad though. but thanks!
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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