Increasing and Decreasing Intervals

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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) rises as x increases.

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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) falls as x increases.

Front

How do you determine if a function is increasing or decreasing on an interval?

Back

You can determine this by analyzing the slope of the function's graph: if the slope is positive, the function is increasing; if negative, it is decreasing.

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-values) does not change as x varies within that interval.

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Front

What is the significance of critical points in determining intervals of increase or decrease?

Back

Critical points are where the 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 before and after a critical point to determine if the function is increasing or decreasing.

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Back

At x=3, the function may either reach a maximum or change to a decreasing interval.

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.