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) changes within that interval.

Front

How do you determine where a function is increasing or decreasing?

Back

To determine where a function is increasing or decreasing, analyze the function's derivative: if the derivative is positive, the function is increasing; if negative, it is decreasing.

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 potential intervals of increase or decrease.

Front

If a function is increasing on the interval (1, ∞), what does this imply about its behavior?

Back

It implies that for every x-value greater than 1, the function's output is greater than the output for any x-value less than 1.

Front

What does the notation (-∞, ∞) represent in terms of intervals?

Back

The notation (-∞, ∞) represents all real numbers, indicating that the function is defined and can take any value.

Front

How can you express the interval where a function is decreasing?

Back

The interval where a function is decreasing can be expressed in interval notation, such as (a, b), where 'a' and 'b' are the endpoints of the interval.

Front

What is the difference between open and closed intervals?

Back

An open interval (a, b) does not include its endpoints, while a closed interval [a, b] includes its endpoints.

Front

If a function is decreasing on the interval (15, 40), what does this indicate about its values?

Back

It indicates that as x moves from 15 to 40, the function's output values are getting smaller.