I'm given an equation and asked to find the following:
- Domain
- Critical points
- Inflection points
- Asymptotes
The function is:
$y = 2 + 9x + 3x^2 -x^3$
It has been quite awhile since I have done this sort of problem so I'm a bit rusty. Can someone check my work and explain the missing parts?
- Domain
All Real
- Critical Points:
Find derivative:
$ y' = -3x^2 + 6x + 9$
Set equal to 0:
$ 3x^2 - 6x - 9 = 0 $
$ (3x + 3)(x - 3) = 0$
$ x = -1, x = 3$
Corresponding points: (-1, -3) & (3,30)
- Inflection Points:
Take second derivative:
$ y'' = 6x - 6$
Set it to 0:
edit (fix typo)
$ x = 1 $
Corresponding point: (1, 13)
- Asymptotes
None