3.5 Intervals of increase and decrease

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What is an interval of increase?

Back

An interval of increase is a range of x-values where the function's output (y-values) is rising as x increases.

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What is an interval of decrease?

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An interval of decrease is a range of x-values where the function's output (y-values) is falling as x increases.

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What does it mean for a function to have an absolute maximum?

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A function has an absolute maximum if there is a point in its domain where the function value is greater than or equal to all other values in that domain.

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What does it mean for a function to have an absolute minimum?

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A function has an absolute minimum if there is a point in its domain where the function value is less than or equal to all other values in that domain.

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

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To determine where a function is increasing or decreasing, analyze the first derivative of the function. If the derivative is positive, the function is increasing; if negative, it is decreasing.

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What is the significance of critical points in a function?

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Critical points are where the derivative is zero or undefined. They help identify potential local maxima, minima, and points of inflection.

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What is a constant function?

Back

A constant function is a function that does not change its value; it has the same output for every input.

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What does it mean for a function to be constant on an interval?

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A function is constant on an interval if it does not increase or decrease; its output remains the same for all x-values in that interval.

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What is the first derivative test?

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The first derivative test is a method used 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.

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What is the difference between local and absolute extrema?

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