Find the real number in the closed interval [0.5, 1.5] such that...

[kate88]

Hi,


I have a homework question that I don't understand what it's asking me to do. I thought it was about maxima and minima, but I have not been given a function.


The question says; Find the real number in the closed interval [0.5, 1.5] such that the sum of this number and
its reciprocal is:
(i) as small as possible. (ii) as large as possible. Justify your answer in each case?


Can anybody walk me through what I am meant to do here?


Thanks!

 

[HallsofIvy]

You are "given a function". For number x, "the sum of this number and its reciprocal" is \(\displaystyle x+ \frac{1}{x}\).