the second derivetavie, ie f''(x) determines CONCAVITY, as it determines teh RATE OF CHANGE OF THE GRADIENT OF THE TANGENT, if f''(x) >0, the curve is concave up at that point, if f''(x)<0, the curve is CONCAVE DOWN at theat point, and if f''(x)=0, it is MOST PORBABLY, and in most cases, a point...