nedgangsfunksjon

A nedgangsfunksjon, or decreasing function, is a mathematical concept describing a function where the output value decreases as the input value increases. More formally, a function f is decreasing on an interval if for any two numbers x1 and x2 in that interval, if x1 < x2, then f(x1) > f(x2). This means that as you move to the right along the x-axis, the graph of the function goes downwards.

The opposite of a decreasing function is an increasing function, where the output value increases as the input value increases. Some functions can be strictly decreasing, meaning f(x1) > f(x2) for all x1 < x2, while others might be non-increasing, allowing f(x1) >= f(x2) for all x1 < x2.

In calculus, a function is typically decreasing on an interval if its derivative is negative over that interval. For example, the function f(x) = -x is a decreasing function because for any x1 < x2, -x1 > -x2. Another common example is f(x) = 1/x for x > 0. As x increases, 1/x decreases. Understanding whether a function is increasing or decreasing is fundamental for analyzing its behavior, finding local extrema, and sketching its graph.