I have a problem where I need to find where the function is increasing/decreasing, critical values, concavity etc... But I think my first derivative may be wrong.

Question:

Using the quotient formula, I have the following:

So to find my critical points, I set my numerator to 0.

I also set my numerator to 0 (something to do with vertical asymtotes but I am not sure why we do this)

Using a number line, I think the function will be:

Decreasing:(-infinity, -.11) U (1.21, infinity)

Increasing:(-.11,1.21)

Correct?

I didn't want to go any further to test for concavity just in case my 1st derivative was wrong.

TIA