Rules to Check Increasing and Decreasing Functions
In calculus, the increasing function can be defined in terms of the slope of any curve as an increasing function always has a positive slope i.e., dy/dx > 0. To define increasing function more formally, let us consider f to be a function that is continuous on the interval [p, q] and differentiable on the open interval (p, q), then
Function f is increasing in [p, q] if f′(x) > 0 for each x ∈ (p, q).
As decreasing function always has a negative slope, thus a decreasing function can be defined in terms of the slope of any curve i.e., dy/dx < 0. For a more formal definition of the decreasing function, let us consider f to be a function that is continuous on the interval [p, q] and differentiable on the open interval (p, q), then
Function f is decreasing in [p, q] if f′(x) < 0 for each x ∈ (p, q).
Increasing and Decreasing Functions
If you’re studying calculus, then you’re probably familiar with the concepts of increasing and decreasing functions. These terms refer to the behavior of a function as its input values change. Specifically, an increasing function is one that becomes larger as its input values increase, while a decreasing function is one that becomes smaller as its input values increase. Understanding these concepts is crucial for solving a variety of calculus problems, from finding maximum and minimum values to understanding the behavior of graphs.
In this article, we’ll delve deeper into increasing and decreasing functions, exploring how to identify them, and how to use them to solve problems in calculus.
Table of Content
- Increasing Function Definition
- Decreasing Function Definition
- Constant Function Definition
- Rules to Check Increasing and Decreasing Functions
- Graph of Increasing, Decreasing, and Constant Function
- Properties of Increasing & Decreasing Functions
- How to Find Increasing and Decreasing Intervals
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