Concavity, convexity and points of inflexion Submitted By ... to concavity in passing through the point . Practice questions. These inflection points are places where the second derivative is zero, and the function changes from concave up to concave down or vice versa. P Point of inflection . If the graph of flies above all of its tangents on an interval I, then it is called concave upward (convex downward) on I. Inflection points are points on the graph where the concavity changes. If P(c, f(x))is a point the curve y= f (x) such that f ‘() , Definition If f is continuous ata and f changes concavity ata, the point⎛ ⎝a,f(a)⎞ ⎠is aninflection point of f. Figure 4.35 Since f″(x)>0for x