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
Cylindrical lens Cylindrical lens A cylindrical lens is a lens which focuses light into a line instead of a point, as a spherical lens would. The curved face or faces of a cylindrical lens are sections of a cylinder, and focus the image passing through it into a line parallel to the intersection of the surface of the lens and a plane tangent to it. The lens compresses the image in the direction perpendicular to this line, and leaves it unaltered in the direction parallel to it (in the tangent plane). In a light sheet microscope, a cylindrical lens is placed in