Increasing and Decreasing Functions

Define Increasing Function.

An increasing function is a function where if you take two input values, the function value at the higher input value will be greater than or equal to the function value at the lower input value.

Define Decreasing Function.

A decreasing function is a function where if you take two input values, the function value at the higher input value will be less than or equal to the function value at the lower input value.

How to tell if Any Given Function is Increasing or Decreasing?

To determine if a function is increasing or decreasing, you can look at the sign of the first derivative. If the first derivative is positive, then the function is increasing. If the first derivative is negative, then the function is decreasing.a

Can a Function be both Increasing and Decreasing?

No, a function cannot be both increasing and decreasing. If a function is increasing on an interval, it cannot be decreasing on the same interval, and vice versa. However, a function can have different intervals of increasing and decreasing behavior.

What is a Strictly Increasing Function?

A strictly increasing function is a function where the value of the function strictly increases as the input value increases. In other words, if you take two input values, the function value at the higher input value will always be greater than the function value at the lower input value.

What is a Strictly Decreasing Function?

A strictly decreasing function is a function where the value of the function strictly decreases as the input value increases. In other words, if you take two input values, the function value at the higher input value will always be less than the function value at the lower input value.

What is a Monotonic Function?

A monotonic function is a function that is either strictly increasing or strictly decreasing.

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.