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?