Find the extreme points of the following functions. Specify if the extremum is a maximum or minimum. Find the extreme values.`y = x^2 + 2x +3`

Explanation

`y = x^2 + 2x + 3
`dy/dx = 2x + 2, (d^2y)/dx^2 = 2`
For extremum, `dy/dx = 0`
`rArr 2x +2 2 = 0 rArr = - 1` is the extreme point.
Now `d^2/dx y/2](_x = -1) = 2 gt 0`
Thus the function attains minimum at `x = - 1`.
The minimum value = `1 - 2 + 3 = 2`.