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 identify increasing intervals on a graph?

Back

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

Front

How do you identify decreasing intervals on a graph?

Back

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

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 the input varies. This means the slope is zero.

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 a function changes from increasing to decreasing or vice versa.

Front

How can you find the increasing intervals algebraically?

Back

To find increasing intervals, take the derivative of the function and solve for where the derivative is greater than zero.

Front

How can you find the decreasing intervals algebraically?

Back

To find decreasing intervals, take the derivative of the function and solve for where the derivative is less than zero.

Front

What is a local maximum?

Back

A local maximum is a point where the function value is higher than all nearby points, indicating a peak in the graph.

Front

What is a local minimum?

Back

A local minimum is a point where the function value is lower than all nearby points, indicating a trough in the graph.

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 it is a local maximum or minimum.