SOLUTION: Solve the optimization problem. Minimize S = x + 17y with xy = 17 and both x and y > 0.

Then your function to minimize is


S =  = .


Take the derivative on x and equate it to zero:


1 - 289/x^2 = 0  ====>  x^2 = 289  ====>  x = +/-17.


Answer.  The local extremum values of x  are  17  and  -17.


         In the domain  x > 0  only the solution x= 17 works.






Plot of the function  S =