Increasing and Decreasing Intervals

Front

What are increasing intervals in a function?

Back

Increasing intervals are ranges of the independent variable (x-values) where the function's output (y-values) is rising as x increases.

Front

What are decreasing intervals in a function?

Back

Decreasing intervals are ranges of the independent variable (x-values) where the function's output (y-values) is falling 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 line 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 line falls as you move from left to right).

Front

What is the notation for intervals?

Back

Intervals are typically written in parentheses or brackets. For example, (a, b) means all numbers between a and b, not including a and b.

Front

What does the interval (2, 4) signify?

Back

The interval (2, 4) signifies that the function is either increasing or decreasing between the x-values of 2 and 4, not including the endpoints.

Front

What does the interval (−∞, 1) signify?

Back

The interval (−∞, 1) signifies that the function is either increasing or decreasing for all x-values less than 1.

Front

What is the significance of endpoints in intervals?

Back

Endpoints can indicate where a function changes from increasing to decreasing or vice versa. They can be included or excluded based on the context.

Front

How can you determine if a function is increasing or decreasing using its derivative?

Back

If the derivative of a function is positive over an interval, the function is increasing. If the derivative is negative, the function is decreasing.

Front

What is the relationship between critical points and increasing/decreasing intervals?

Back

Critical points, where the derivative is zero or undefined, can indicate potential changes in increasing or decreasing behavior.