Extrema (Maximum/Minimum)

Front

What is the definition of extrema in mathematics?

Back

Extrema refer to the maximum and minimum values of a function, which can occur at specific points in its domain.

Front

What is a maximum value?

Back

The maximum value of a function is the highest point on its graph, representing the largest y-value.

Front

What is a minimum value?

Back

The minimum value of a function is the lowest point on its graph, representing the smallest y-value.

Front

How do you find the maximum or minimum value of a function?

Back

To find extrema, you can use calculus techniques such as taking the derivative and setting it to zero to find critical points.

Front

What is a critical point?

Back

A critical point is a point on the graph of a function where the derivative is zero or undefined, indicating potential maxima or minima.

Front

What is the difference between absolute and relative extrema?

Back

Absolute extrema are the highest or lowest values over the entire domain, while relative extrema are the highest or lowest values within a specific interval.

Front

What is the first derivative test?

Back

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

Front

What is the second derivative test?

Back

The second derivative test is a method used to determine the concavity of a function at a critical point, helping to classify it as a maximum or minimum.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if the y-values rise as the x-values increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if the y-values fall as the x-values increase.