increasing, decreasing, and constant intervals

Front

What is an increasing interval in a function?

Back

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

Front

What is a decreasing interval in a function?

Back

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

Front

What does it mean for a function to be constant on an interval?

Back

A function is constant on an interval if its output (y-values) does not change as x varies within that interval.

Front

How can you identify increasing and decreasing intervals from a graph?

Back

Increasing intervals are where the graph rises from left to right, while decreasing intervals are where the graph falls from left to right.

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 intervals of increase or decrease.

Front

What is the first derivative test?

Back

The first derivative test is a method used to determine whether a function is increasing or decreasing on an interval by analyzing the sign of its derivative.

Front

How do you find the intervals of increase and decrease algebraically?

Back

To find intervals of increase and decrease, take the derivative of the function, set it to zero to find critical points, and test the sign of the derivative in the intervals created.

Front

What is the relationship between the first derivative and the behavior of a function?

Back

If the first derivative is positive, the function is increasing; if negative, the function is decreasing; if zero, the function may be constant or have a critical point.

Front

What does it mean if a function has no decreasing intervals?

Back

If a function has no decreasing intervals, it means that the function is either increasing or constant for all x-values.

Front

Can a function be both increasing and decreasing on the same interval?

Back

No, a function cannot be both increasing and decreasing on the same interval; it can only exhibit one behavior at a time.