Increasing and Decreasing Intervals

Front

What are increasing intervals in a function?

Back

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

Front

What are decreasing intervals in a function?

Back

Decreasing intervals are the ranges of x-values where the function's output (y-value) 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 graph rises 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 graph falls from left to right).

Front

What is the notation for intervals?

Back

Intervals are typically written in parentheses or brackets, e.g., (a, b) for open intervals and [a, b] for closed intervals.

Front

What does the interval (2, 4) signify?

Back

It signifies that the function is increasing or decreasing between x = 2 and x = 4, not including the endpoints.

Front

What does the interval [1, 3] signify?

Back

It signifies that the function is increasing or decreasing between x = 1 and x = 3, including the endpoints.

Front

If a function is increasing on (3, 5), what can you say about its derivative?

Back

The derivative of the function is positive on the interval (3, 5).

Front

If a function is decreasing on (1, 2), what can you say about its derivative?

Back

The derivative of the function is negative on the interval (1, 2).

Front

What is the significance of critical points in determining intervals?

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.