Relative Extrema

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What is a LOWER BOUND?

Back

A lower bound is some number that is less than or equal to every value in the range of a function.

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How many extrema (maxes and mins) can a function have?

Back

A function can have multiple extrema; for example, a function can have 3 extrema.

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What does it mean for a function to be bounded above?

Back

A function is bounded above if there exists a number that is greater than or equal to every value in the range of the function.

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What does it mean for a function to be bounded below?

Back

A function is bounded below if there exists a number that is less than or equal to every value in the range of the function.

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What does it mean for a function to be unbounded?

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A function is unbounded if it does not have an upper or lower bound; it can take on infinitely large or small values.

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What is a relative maximum?

Back

A relative maximum is a point in the domain of a function where the function value is greater than the values of the function at nearby points.

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What is a relative minimum?

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A relative minimum is a point in the domain of a function where the function value is less than the values of the function at nearby points.

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How can you determine if a function has relative extrema?

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You can determine if a function has relative extrema by finding the critical points where the derivative is zero or undefined.

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What is the first derivative test?

Back

The first derivative test is a method used to determine whether a critical point is a relative maximum, minimum, or neither by analyzing the sign of the derivative before and after the point.

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What is the second derivative test?

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The second derivative test is a method used to determine the concavity of a function at a critical point to classify it as a relative maximum or minimum.