Extrema,Increasing, and Decreasing

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-value) is rising 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-value) is falling as x increases.

Front

How do you determine the increasing intervals of a function?

Back

To find increasing intervals, identify where the derivative of the function is positive.

Front

How do you determine the decreasing intervals of a function?

Back

To find decreasing intervals, identify where the derivative of the function is negative.

Front

What is a local maximum?

Back

A local maximum is a point where the function value is higher than all nearby points.

Front

What is a local minimum?

Back

A local minimum is a point where the function value is lower than all nearby points.

Front

How do you find local maxima and minima?

Back

Local maxima and minima can be found using the first derivative test or the second derivative test.

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 max or min.

Front

What is the second derivative test?

Back

The second derivative test uses the second derivative of a function to determine concavity and identify local extrema.

Front

What does it mean if the first derivative is zero at a point?

Back

If the first derivative is zero at a point, it indicates a potential local maximum, minimum, or inflection point.