Problem+4+Alex+G,+Yutong

Question: Find a positive number such that the sum of the number and its reciprocal is as small as possible.

For this question, I set f(x)=x + 1/x The domain is that x>0

Derive this function to get f'(x)= 1 - 1/x^2

Set this equal to 0 0=1- 1/x^2 1/x^2=1 x=1 or x=-1 Since the domain is that x>0, x=1 is the answer we accept.

Don't forget that you are looking for the absolute minimum, so you need to take into account what is happening at the endpoints (Yutong, why don't you handle this part?) so...if the endpoints of the domain is included in this situation (CAN x = 0 and still be positive), just plug them into the objective function...otherwise, take the limit as x approaches these outer reaches!

The limit as x approaches 0 is infinity because 1 over a small possitive number is infinity. therefore the sum of x+1/x is infinity. What about the other endpoint (and what is it?) You need to take both endpoints into account !