Increasing/Decreasing/extrema Extra credit

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as the input values (x) increase, the output values (f(x)) also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as the input values (x) increase, the output values (f(x)) decrease.

Front

What are extrema in a function?

Back

Extrema are the maximum and minimum values of a function. A maximum is the highest point, while a minimum is the lowest point on a graph.

Front

How can you determine where a function is increasing or decreasing?

Back

You can determine where a function is increasing or decreasing by analyzing its derivative. If the derivative is positive, the function is increasing; if negative, it is decreasing.

Front

What is the first derivative test?

Back

The first derivative test is a method used to determine local extrema by analyzing the sign of the derivative before and after a critical point.

Front

What is a critical point?

Back

A critical point occurs where the derivative of a function is zero or undefined, indicating potential extrema.

Front

How do you find the extrema of a function graphically?

Back

To find extrema graphically, look for the highest and lowest points on the graph of the function.

Front

What is the difference between local and global extrema?

Back

Local extrema are the highest or lowest points in a specific interval, while global extrema are the highest or lowest points over the entire domain of the function.

Front

What does it mean if a function is neither increasing nor decreasing?

Back

A function is neither increasing nor decreasing if it remains constant over an interval or has no clear trend.

Front

What is the significance of the second derivative in determining concavity?

Back

The second derivative indicates the concavity of a function. If the second derivative is positive, the function is concave up; if negative, it is concave down.