Solve Optimization Problems | Derivative of T(y) | Maximal/Minimal Area"

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Homework Statement


look at jpg attachment


Homework Equations



T(y)=(z-y/r)+(sqrt(x^2+y^2)/s)
ac=z
bc=x
dc=y
ab=w
im having trouble taking the derivative of T(y) and how to solve it

on the second one i think there is no maximal area but there is a minimal but not sure how to start it
 

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nevermind i figured them out
 
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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