Properties of Increasing & Decreasing Functions
Some helpful algebraic properties of Increasing & Decreasing Functions are as follows:
- Additive property. If the functions f and g are increasing/decreasing on the interval (a, b), then the sum of the functions f + g is also increasing/decreasing on this interval.
- Opposite property. If the function f is increasing/decreasing on the interval (a, b), then the opposite function, -f, is decreasing/increasing.
- Inverse property. If the function f is increasing/decreasing on the interval (a, b), then the inverse function, 1/f, is decreasing/increasing on this interval.
- Multiplicative property. If the functions f and g are increasing/decreasing and not negative on the interval (a, b), then the product of the functions is also increasing/decreasing.
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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