Determine the largest open intervals of the domain over which each function is b) decreasing. See Example 9.

Key Concepts

Decreasing Functions

A function is considered decreasing on an interval if, for any two points within that interval, the function's value at the first point is greater than its value at the second point. This means that as the input values increase, the output values decrease. Identifying decreasing intervals is crucial for understanding the behavior of functions and their graphs.

Critical Points

Critical points are values in the domain of a function where the derivative is either zero or undefined. These points are significant because they can indicate local maxima, minima, or points of inflection. In the context of decreasing functions, critical points help determine where the function changes from increasing to decreasing or vice versa.

Interval Notation

Interval notation is a mathematical notation used to represent a range of values. It uses parentheses and brackets to indicate whether endpoints are included (closed intervals) or excluded (open intervals). Understanding interval notation is essential for accurately expressing the domain of decreasing intervals in functions, as it provides a clear way to communicate which values are part of the interval.