Hello
I have a derivative (of a function) which I'm using to find out at what values of x the original function is increasing or decreasing. I understand the process. But the derivative is this:
(-2) / (x^3) > 0
(I hope that's written clearly.) I can divide both sides by -1, which also changes the direction of the inequality sign. I can then divide both sides by 2, which leaves me with:
(1)/(x^3) < 0
But I CAN'T divide or multiply both sides by x, because I don't know if the variable is positive or negative. So how do I solve for x? How can I take x out of the denominator? How do I find what x is greater or less than?
This is a question from A-Level Math Core 2. Perhaps I'm misunderstanding the question?
EDIT: Because I'm only solving for what value x is higher or lower than, perhaps in this case I can multiply/divide by a variable, because I will be using both x> and x< to determine when the original function is increasing/decreasing. Am I correct? (I hope I'm explaining myself well.)