the problem is in the attached pdf file.concavity.PDF
Questions about concavity are best answered with the second derivative, which you don't seem to have found. I'd recommend finding the second derivative, and then using the second derivative test:
As you can see, the plus-sign eyes (second derivative is positive) correspond to concave up. The minus-sign eyes (second derivative is negative) correspond to concave down. The zero eyes (second derivative is zero) is a very confused individual: you could have it concave down (one eyebrow), or concave up (the other eyebrow) or a point of inflection (the mouth). That is, if the second derivative is zero, you don't know what's happening there in terms of concavity.
Does that help?