HW Flashcardizz: Increasing and Decreasing Intervals

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-values) decreases as x increases.

Front

What does it mean if a function is decreasing across the entire domain?

Back

It means that for every x-value in the domain, the function's output is always decreasing.

Front

How can you identify a decreasing interval on a graph?

Back

A decreasing interval can be identified on a graph where the slope of the function is negative.

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-values) increases as x increases.

Front

How can you identify an increasing interval on a graph?

Back

An increasing interval can be identified on a graph where the slope of the function is positive.

Front

What does it mean if a function is increasing across the entire domain?

Back

It means that for every x-value in the domain, the function's output is always increasing.

Front

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

Back

Critical points are where the function's derivative is zero or undefined, indicating potential changes in increasing or decreasing behavior.

Front

How do you find the intervals of increase and decrease using derivatives?

Back

By finding the derivative of the function, setting it to zero, and analyzing the sign of the derivative on intervals defined by the critical points.

Front

What is the relationship between the first derivative and increasing/decreasing intervals?

Back

If the first derivative is positive, the function is increasing; if negative, the function is decreasing.

Front

What does it mean if a function has no decreasing intervals?

Back

It means that the function either increases or remains constant for all x-values in its domain.