In this article, we will study the concept of increasing and decreasing functions, their properties, graphical representation, and theorems to test for increasing and decreasing functions along …

Strictly Increasing (and Strictly Decreasing) functions have a special property called "injective" or "one-to-one" which simply means we never get the same "y" value twice. Why is this useful? …

Nov 27, 2025 · In simple words, a decreasing function is a type of function where, with increasing input (or the independent variable), the output value decreases (or the value of the function).

May 27, 2025 · Decreasing functions are a fundamental concept in calculus, playing a crucial role in understanding how functions behave and change. In this section, we'll explore the definition, …

Dec 3, 2025 · A function f (x) decreases on an interval I if f (b)<=f (a) for all b>a, where a,b in I. If f (b)<f (a) for all b>a, the function is said to be strictly decreasing.

By partitioning the number line into intervals on which a function's derivative is positive and negative, the behavior of a function can be determined based on the sign of the derivative on …

Dec 1, 2025 · In this lesson we will consider the function values in between extrema (extremes: minimums or maximums), focusing on where function values are increasing or decreasing. A …

A decreasing function is a function in which the values of the dependent variable decrease as the values of the independent variable increase. In other words, as you move from left to right on …

Sep 13, 2025 · To grasp what a decreasing function is, let’s start with its foundational element: the function itself. What is a Function? At its core, a function (mathematics) is like a reliable rule or …

Dec 6, 2025 · The first derivative of a function reveals where the original function is increasing, decreasing, or remains monotonic over specific intervals.