#1**+3 **

x^3 -2x^2 - 3x < 0

Let's solve this

x^3 - 2x^2 - 3x = 0 factor

x( x^2 - 2x - 3) = 0

x( x - 3) ( x + 1) = 0

Set each factor to 0 and solve for x and the solutions are

x = 0 , x = 3 and x = -1

We have four possible solution intervals

(-inf, -1), ( - 1, 0) , (0, 3) and (3, inf )

This graph shows that the intervals in red are the correct solution intervals :

https://www.desmos.com/calculator/z8f6gksyuq

CPhill
Nov 14, 2017