Positive/Negative and Increasing/Decreasing Intervals

Front

What is a positive interval in a function?

Back

A positive interval is a range of x-values where the function's output (y-value) is greater than zero.

Front

What is a negative interval in a function?

Back

A negative interval is a range of x-values where the function's output (y-value) is less than zero.

Front

How do you identify increasing intervals in a function?

Back

Increasing intervals are ranges of x-values where the function's output (y-value) is rising as x increases.

Front

How do you identify decreasing intervals in a function?

Back

Decreasing intervals are ranges of x-values where the function's output (y-value) is falling as x increases.

Front

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

Back

A function is constant on an interval if its output (y-value) does not change as x varies within that interval.

Front

What is the notation for an open interval?

Back

An open interval is denoted by parentheses, e.g., (a, b), meaning a and b are not included.

Front

What is the notation for a closed interval?

Back

A closed interval is denoted by brackets, e.g., [a, b], meaning a and b are included.

Front

How can you determine the intervals of increase or decrease from a graph?

Back

By observing the slope of the graph: if the slope is positive, the function is increasing; if negative, it is decreasing.

Front

What is the significance of critical points in determining intervals?

Back

Critical points are where the function's derivative is zero or undefined; they help identify where the function changes from increasing to decreasing or vice versa.

Front

What is the first derivative test?

Back

The first derivative test involves analyzing the sign of the derivative to determine whether a function is increasing or decreasing on intervals.