Problem: For what values of is the curve concave downward?

OK, so this calls for a 2nd derivative test. So this is what I did:

. That was easy. But now we have a product.

. Now, if I'm looking for concave downward, I want the value of the expression to be ,

. We know ; then we must be really looking for

That's how far I got with it. The answer is supposed to be the interval .

Did I botch something somewhere?