Flash Lesson Tuesday 05.02.23 Increasing & decreasing Intervals

Front

What is an increasing interval in a function?

Back

An increasing interval is a range of x-values where the function's output (y-values) rises as x increases.

Front

What is a decreasing interval in a function?

Back

A decreasing interval is a range of x-values where the function's output (y-values) falls as x increases.

Front

How do you determine increasing and decreasing intervals from a graph?

Back

Identify the sections of the graph where the slope is positive (increasing) or negative (decreasing).

Front

What does it mean if a function is constant on an interval?

Back

A function is constant on an interval if its output does not change as x varies within that interval.

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.

Front

Back

Find the derivative, set it to zero to find critical points, and test intervals to determine where the function is increasing.

Front

What is the derivative of a function?

Back

The derivative of a function represents the rate of change of the function's output with respect to its input.

Front

What is the first derivative test?

Back

The first derivative test is used to determine whether a critical point is a local maximum, minimum, or neither by analyzing the sign of the derivative.

Front

What is the role of the second derivative in analyzing intervals?

Back

The second derivative indicates the concavity of the function and helps determine the nature of critical points.

Front

How do you express an interval in interval notation?

Back

Interval notation uses parentheses and brackets to denote open and closed intervals, e.g., (a, b) or [a, b].