Konkávnost

Konkávnost is a geometric property describing the curvature of a curve or surface. A curve is considered concave upward or convex downward if it bends in a way that resembles a bowl facing upwards. Conversely, a curve is concave downward or convex upward if it bends like a bowl facing downwards. The concavity of a function's graph is determined by its second derivative. If the second derivative of a function is positive over an interval, the function is concave up on that interval. If the second derivative is negative, the function is concave down. Points where the concavity changes are called inflection points.

In the context of functions, concavity is a crucial concept for understanding their behavior. It helps in identifying local extrema, as a function with a local maximum is typically concave down at that point, and a function with a local minimum is typically concave up. This property is widely used in calculus for curve sketching and optimization problems. For surfaces, concavity describes whether a point on the surface is locally a minimum or maximum, or a saddle point, based on the curvature in different directions. The term "konkávnost" is the direct translation of concavity, commonly used in languages like German and Dutch, and is understood in broader mathematical contexts.