Increasing and Decreasing Intervals

Front

What are increasing and decreasing intervals in a function?

Back

Increasing intervals are ranges where the function's output (y-value) rises as the input (x-value) increases. Decreasing intervals are ranges where the function's output falls as the input increases.

Front

How do you determine increasing intervals from a graph?

Back

Identify sections of the graph where the slope is positive (rising). The x-values of these sections represent the increasing intervals.

Front

How do you determine decreasing intervals from a graph?

Back

Identify sections of the graph where the slope is negative (falling). The x-values of these sections represent the decreasing intervals.

Front

What is the notation for intervals?

Back

Intervals are expressed in parentheses or brackets. For example, (a, b) means all numbers between a and b, not including a and b. [a, b] includes a and b.

Front

What does the interval (−∞, c) represent?

Back

This interval includes all real numbers less than c, extending indefinitely to the left on the number line.

Front

What does the interval (c, ∞) represent?

Back

This interval includes all real numbers greater than c, extending indefinitely to the right on the number line.

Front

How do you find the increasing interval from a function's derivative?

Back

If the derivative of a function is positive in an interval, then the function is increasing in that interval.

Front

How do you find the decreasing interval from a function's derivative?

Back

If the derivative of a function is negative in an interval, then the function is decreasing in that interval.

Front

What is a critical point in the context of increasing and decreasing intervals?

Back

A critical point is where the derivative is zero or undefined. It helps identify potential local maxima or minima, which can indicate changes in increasing or decreasing behavior.

Front

What is the first derivative test?

Back

The first derivative test involves analyzing the sign of the derivative before and after a critical point to determine if the function is increasing or decreasing.