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What is the definition of Absolute Minimum?

Back

The Absolute Minimum of a function is the lowest point over its entire domain. It is the smallest value that the function can take.

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What is the definition of Absolute Maximum?

Back

The Absolute Maximum of a function is the highest point over its entire domain. It is the largest value that the function can take.

Front

What is a Relative Maximum?

Back

A Relative Maximum is a point where the function value is higher than the values of the function at nearby points, but not necessarily the highest overall.

Front

What is a Relative Minimum?

Back

A Relative Minimum is a point where the function value is lower than the values of the function at nearby points, but not necessarily the lowest overall.

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How do you find Absolute Maxima and Minima?

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To find Absolute Maxima and Minima, evaluate the function at critical points (where the derivative is zero or undefined) and at the endpoints of the interval.

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What is the difference between Absolute and Relative Extrema?

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Absolute Extrema refer to the highest or lowest points over the entire domain, while Relative Extrema refer to the highest or lowest points in a specific interval.

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What does it mean if a function has no Absolute Minimum?

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If a function has no Absolute Minimum, it means that the function does not reach a lowest value within its domain, often due to the function approaching negative infinity.

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What does it mean if a function has no Absolute Maximum?

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If a function has no Absolute Maximum, it means that the function does not reach a highest value within its domain, often due to the function approaching positive infinity.

Front

What is a critical point?

Back

A critical point of a function is a point in its domain where the derivative is zero or undefined, which may indicate a local maximum or minimum.

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How can you determine if a critical point is a maximum or minimum?

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You can use the First Derivative Test or the Second Derivative Test to determine if a critical point is a maximum or minimum.