Concave function the graph of formula_1 is above the straight line joining the points formula_15 and formula_16. A function formula_1 is quasiconcave if the upper contour sets of the function formula_18 are convex sets. 1. A differentiable function is (strictly) concave on an interval if and only if its derivative function is (strictly) monotonically decreasing on that interval, that is, a concave function has a non-increasing (decreasing) slope. 2. Points where concavity changes (between concave and convex) are inflection points. 3. If is twice-differentiable, then is concave if and only if is non-positive (or, informally, if the "acceleration" is non-positive). If its
Focal cloud Focal cloud A focal cloud is the collection of focal points of an "imperfect" lens or parabolic reflector whether optical, electrostatic or electromagnetic. This includes parabolic antennas and lens-type reflective antennas of all kinds. The effect is analogous to the circle of confusion in photography. In a perfect lens or parabolic reflector, rays parallel to the device's axis striking the lens or reflector all pass through a single point, the focal point. In an imperfectly constructed lens or reflector, rays passing through different parts of the element do not converge to a single point but have different focal points. The