Well, you've already done the work. The function is increasing as long as . Since for all real (non-zero) x, we can multiply on both sides by and get [tex]x^3- x> 0[\math]. That factors as . The simplest way to determine where the derivative is positive or negative is to recognize that it can change from one to the other only where it is negative. And that occurs only at x=-1, x= 0, and x= 1. Choose one value for x in each of the intervals , -1< x< 0, 0< x< 1, and to see whether the derivative is positive or negative in that interval.as f`(x)=1+2/x^3. Having said that, the graph on the left side of the y axis seems to travel in a positive direction until it gets to the y axis, then goes to -infinity. The graph on the right side of the y axis seems to go from o to infinity. Am I doing this correctly? Is the increasing interval (o, to infinity)?