Find the maximum or minimum values of the function `y=x+1/x for xgt0`.

Explanation

Let `f(x) = x+1/x`
`rArr f'(x) =1 - 1/x^(2)`
From maxima or minima
` f(x) = 0`
`rArr 1-1/x^(2) = 0`
`rArr x=1,-1`
Now ` f''(x_ = 2/x^(3)`
`"At " x= 1`,
`f''(1) = 2/(1)^(3) = 2 gt 0`
`:. F(x)" is minimum at "x=1`
and minimum value = `f(1) = 1+1/1 = 2`
`"At " x= -1`.
`f''(-1) = 2/(-1)^(3) =-2 lt 0`
`:. f(x)" is maximum at "x = - 1`
and maximum value = `f(-1)=-1-1=-2`
Therefore the maximum value of the function is ` -2 "at" x=-1` and minimum value is 2 at x = 1.