Question

How do I get -9x^-2+1 to factor out so I can identify the interval on which the function is increasing or decreasing.?

The original equation is y=x+(9/x)

Answer 1

Step 1 : 

The function is .

Differentiate with respect to x.

Determination of critical points :

The function is undefined when .

Equate to zero:

The critical points are and .

Step 2 :

Consider the test intervals as and .

Thus, The function is increasing on the intervals and .

And The function is decreasing on the intervals and .

Solution :

The function is increasing on the intervals and .

The function is decreasing on the intervals and .