Positive/Negative and Increasing/Decreasing 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) increases 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) decreases as x increases.

Front

How do you identify increasing intervals on a graph?

Back

Look for sections of the graph where the slope is positive (the graph rises as you move from left to right).

Front

How do you identify decreasing intervals on a graph?

Back

Look for sections of the graph where the slope is negative (the graph falls as you move from left to right).

Front

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

Back

A function is constant on an interval if its output does not change as x varies within that interval.

Front

What is the notation for an interval?

Back

Intervals are typically written in parentheses or brackets, e.g., (a, b) for open intervals and [a, b] for closed intervals.

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include their endpoints (e.g., (a, b)), while closed intervals do include their endpoints (e.g., [a, b]).

Front

How can you find the increasing intervals from a function's derivative?

Back

If the derivative of a function is positive on an interval, then the function is increasing on that interval.

Front

How can you find the decreasing intervals from a function's derivative?

Back

If the derivative of a function is negative on an interval, then the function is decreasing on that interval.

Front

What is the significance of critical points in determining intervals?

Back

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