solve the following inequality. write your solutionin interval notation x^3-x<0

Answer 1

x(x-1)(x+1) < 0

The roots are -1,0,1

Since there are no repeated roots, the graph crosses the axis at each root.

So, y<0 for large x<0, so the intervals are

(oo,-1) < 0
(-1,0) > 0
(0,1) < 0
(1,oo) > 0

y<0 for x in (-oo,-1)U(0,1)