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Concavity is the sign of the second derivative. Positive means the curve bends upward like a bowl holding water; negative means it bends downward. The tangent line lies below a concave-up curve and above a concave-down one.
Concavity
f''(x) > 0 concave up; f''(x) < 0 concave down
f'' = 6x − 6, giving 6 at x = 2 (concave up) and −18 at x = −2 (concave down).
Yes. At a critical point, concave up means a minimum and concave down means a maximum.