For x>0, what value of x gives the least sum of x and its reciprocal? Show work.

Answer 1

x+(1/x) = y

y&prime = 1 - 1/x²

set that equal to zero.

You didn't specify that you were in calculus though, so I'll provide a second way.

x + (1/x) = y

if x = 1, then y = 2

if x = 1/2 then y = 5/4>2

if x = 2 then y = 5/4>2

if x = 1/3 then y = 10/3>2

if x = 3 then y = 10/3>2

you can see that as x gets bigger and smaller then 1 y gets bigger then 2, so when x = 1 you have a minimum value