Find the open intervals on which f is increasing and decreasing.

Question

Let f(x)= 2-(2/x)+(6/x²).  Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima).

1. f is increasing on the intervals?

2. f is decreasing on the intervals?

3. the relative maxima of f occur at x=

4. the relative minima of f occur at x=

 

Answer 1

No Minimum, Horizontal asymptote is y=2; Vertical asymptote is x=0, function is increasing from 2+0 at the "point" of minus infinity to plus infinity at the left part of the point x=0; function is increasing from minus infinity at the right part of the point x=0 until horizontal asymptote y=2 (but stays below). Function intersects y=0 at the point x=6.