3.5 Intervals of increase and decrease

Front

What is an interval of increase?

Back

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

Front

What is an interval of decrease?

Back

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

Front

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

Back

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

Front

How can you identify intervals of increase and decrease on a graph?

Back

Intervals of increase are where the graph rises from left to right, and intervals of decrease are where the graph falls from left to right.

Front

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

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.

Front

How do you determine the number of intervals in a function?

Back

Count the distinct sections of the graph where the function is either increasing, decreasing, or constant.

Front

What is the relationship between the first derivative and intervals of increase/decrease?

Back

If the first derivative is positive, the function is increasing; if negative, the function is decreasing.

Front

What does a horizontal line on a graph indicate about the function?

Back

A horizontal line indicates that the function is constant over that interval.

Front

How can you tell if an interval is increasing or decreasing from a table of values?

Back

Look for changes in the y-values: if they increase as x increases, the interval is increasing; if they decrease, the interval is decreasing.

Front

What is the role of endpoints in determining intervals?

Back

Endpoints can affect whether an interval is open or closed and can indicate where a function starts or stops increasing or decreasing.