You have,Originally Posted by pakman
Find the critical points, since the derivative exists everywhere you need to find,
That happens when,
Now, break your problem into intervals (you are going to use the first derivative test).
Considers the intervals, by choosing and point and calculating is derivative and seeing whether positive or negative.
Therefore the function is
Inscreasing on .
Also, from this test we see that a relative maximum occurs at and relative minimum at .
To work with concavity you need to find which is by the quotient rule,
Proceed as before by finding the critical points,
Now divide the intervals into two parts,
and select any points and these intervals and find thier signs.