Find the extreme points of the following functions. Specify if the extremum is a maximum or minimum. Find the extreme values. `y = x + 1/x`

Explanation

`y = x + 1/x`
`dy/dx = 1 - 1/x^2, (d^2y)/dx^2 = 2/x^3`
For extremum `dy/dx = 0`
`rArr 1 - 1/x^2 = 0 rArr x = + - 1` are the extreme points.
Maximum at `x = -1` and minimum at `x=1`
Maximum value = `- 1 -1 = -2`
Minimum value = 2.