Increasing/Decreasing

Front

What is an increasing function?

Back

A function is increasing on an interval if, for any two points in that interval, the function value at the second point is greater than the function value at the first point.

Front

What is a decreasing function?

Back

A function is decreasing on an interval if, for any two points in that interval, the function value at the second point is less than the function value at the first point.

Front

How do you determine the increasing interval of a function?

Back

To determine the increasing interval, find where the derivative of the function is positive.

Front

How do you determine the decreasing interval of a function?

Back

To determine the decreasing interval, find where the derivative of the function is negative.

Front

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

Back

A function is constant on an interval if it does not change value; its derivative is zero on that interval.

Front

What is the significance of critical points in determining increasing/decreasing intervals?

Back

Critical points are where the derivative is zero or undefined; they help identify potential intervals of increase or decrease.

Front

What is the first derivative test?

Back

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

Front

If a function is increasing on the interval (1, 3), what can be said about its behavior at the endpoints?

Back

At the endpoints, the function value at 3 is greater than at 1, indicating an overall increase.

Front

What is the notation for an increasing interval?

Back

Increasing intervals are often denoted in interval notation, such as (a, b) or (-∞, c).

Front

What is the notation for a decreasing interval?

Back

Decreasing intervals are also denoted in interval notation, such as (d, e) or (f, ∞).