Looks like you have a simplification error in the second derivative. You have:
But it should be
then the intervals for concavity all change.
Am I missing something? Thank you so much for your good product and wonderful support!
Dr. Callahan Answered:
You are correct. Thanks for pointing that out.
See the plot of the original equation (a good idea is to look at plots when things are not working out)
From here we can see how it is shaped.
Now if we look at the second derivative, it should be
and look like
which has roots
and looks like
The concavity chart will now show up, down, and up but around the points