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 over which 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 over which the function's output (y-values) is falling as x 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-values) does not change as the input (x-values) varies within that interval.

Front

How do you determine if a function is increasing on an interval?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) < f(x2).

Front

How do you determine if a function is decreasing on an interval?

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) > f(x2).

Front

What is the notation for representing intervals?

Back

Intervals are often represented using parentheses ( ) for open intervals and brackets [ ] for closed intervals.

Front

What does the notation (-∞, 2) represent?

Back

The notation (-∞, 2) represents all real numbers less than 2, extending indefinitely to the left.

Front

What does the notation (1, ∞) represent?

Back

The notation (1, ∞) represents all real numbers greater than 1, extending indefinitely to the right.

Front

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

Back

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

Front

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

Back

By analyzing the slope of the graph: if the graph rises, the function is increasing; if it falls, the function is decreasing.