Increasing and Decreasing Intervals

Front

What is an increasing interval in a function?

Back

An increasing interval is a range of x-values over which the function's output (y-values) increases as x increases.

Front

What is a decreasing interval in a function?

Back

A decreasing interval is a range of x-values over which the function's output (y-values) decreases as x increases.

Front

How do you determine the increasing intervals of a function?

Back

To determine the increasing intervals, find the derivative of the function and identify where it is positive.

Front

How do you determine the decreasing intervals of a function?

Back

To determine the decreasing intervals, find the derivative of the function and identify where it is negative.

Front

What does it mean if a function is constant on an interval?

Back

If a function is constant on an interval, it means that the output (y-values) does not change as the input (x-values) changes within that interval.

Front

What is the significance of critical points in determining intervals of increase or decrease?

Back

Critical points are where the derivative is zero or undefined; they help identify potential locations where the function changes from increasing to decreasing or vice versa.

Front

What is the first derivative test?

Back

The first derivative test is a method used to determine whether a critical point is a local maximum, local minimum, or neither by analyzing the sign of the derivative before and after the critical point.

Front

What is the role of the second derivative in analyzing intervals of increase and decrease?

Back

The second derivative can indicate the concavity of the function and help confirm whether a critical point is a maximum or minimum.

Front

What is the notation for an interval?

Back

An interval is typically denoted using parentheses for open intervals (not including endpoints) and brackets for closed intervals (including endpoints).

Front

How can you express increasing intervals using interval notation?

Back

Increasing intervals can be expressed in interval notation, such as (a, b) or [a, b), indicating the range of x-values where the function is increasing.