Convex function an interval if and only if its second derivative is non-negative there; this gives a practical test for convexity. Visually, a twice differentiable convex function "curves up", without any bends the other way (inflection points). If its second derivative is positive at all points then the function is strictly convex, but the converse does not hold. For example, the second derivative of "f"("x") = "x" is "f" ′′("x") = 12"x", which is zero for "x" = 0, but "x" is strictly convex. 6. If is a convex function of one real variable, and , then is superadditive on the positive
Parallel projection central or perspective projection, in which the rays pass through a fixed point called the "center" or "viewpoint", as this point is moved towards infinity. Put differently, a parallel projection corresponds to a perspective projection with an infinite focal length (the distance between the lens and the focal point in photography) or "zoom". In parallel projections, lines that are parallel in three-dimensional space remain parallel in the two-dimensional projected image. A perspective projection of an object is often considered more realistic than a parallel projection, since it more closely resembles human vision and photography. However, parallel projections are popular in