Intervals of Increase and Decrease

Front

What is an interval of increase?

Back

An interval of increase is a range of values on a graph where the function's output (y-value) rises as the input (x-value) increases.

Front

What is an interval of decrease?

Back

An interval of decrease is a range of values on a graph where the function's output (y-value) falls as the input (x-value) increases.

Front

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

Back

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

Front

How can you identify an interval of increase on a graph?

Back

An interval of increase can be identified on a graph by observing that as you move from left to right, the graph rises.

Front

How can you identify an interval of decrease on a graph?

Back

An interval of decrease can be identified on a graph by observing that as you move from left to right, the graph falls.

Front

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

Back

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

Front

What is a derivative in the context of intervals of increase and decrease?

Back

A derivative represents the rate of change of a function; if the derivative is positive, the function is increasing; if negative, it is decreasing.

Front

What does it mean for a function to have a local maximum?

Back

A local maximum is a point where the function reaches a higher value than at nearby points, indicating a change from increasing to decreasing.

Front

What does it mean for a function to have a local minimum?

Back

A local minimum is a point where the function reaches a lower value than at nearby points, indicating a change from decreasing to increasing.

Front

How do you determine the intervals of increase and decrease from a function's graph?

Back

To determine intervals of increase and decrease, analyze the slope of the graph: rising indicates increasing, falling indicates decreasing.