Just to clarify, is the function you have given ?
If ,
Then
and
So
To solve for local extreme values (maxima and minima), solve
To solve for where the function is increasing, solve
To solve for where the function is decreasing, solve
For concave up and concave down the second derivative is needed.
To find where the function is concave up, solve
To find where the function is concave down, solve
To find where the inflection points, solve