Relative Minimums and Maximums/First Derivative Test

Front

What is a relative maximum?

Back

A relative maximum is a point on a function where the function value is higher than the values of the function at nearby points. It is a local peak.

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What is a relative minimum?

Back

A relative minimum is a point on a function where the function value is lower than the values of the function at nearby points. It is a local trough.

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What does the First Derivative Test help determine?

Back

The First Derivative Test helps determine the relative maximums and minimums of a function by analyzing the sign of the first derivative.

Front

How do you find intervals where a function is increasing?

Back

To find intervals where a function is increasing, identify where the first derivative is positive.

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How do you find intervals where a function is decreasing?

Back

To find intervals where a function is decreasing, identify where the first derivative is negative.

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What is the significance of critical points?

Back

Critical points are where the first derivative is zero or undefined, and they are potential locations for relative maximums and minimums.

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What is the relationship between the first derivative and the graph of a function?

Back

The first derivative indicates the slope of the tangent line to the graph of the function, showing whether the function is increasing or decreasing.

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What does it mean if the first derivative changes from positive to negative at a critical point?

Back

If the first derivative changes from positive to negative at a critical point, it indicates a relative maximum at that point.

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What does it mean if the first derivative changes from negative to positive at a critical point?

Back

If the first derivative changes from negative to positive at a critical point, it indicates a relative minimum at that point.

Front

What is an extremum?

Back

An extremum is a point in a function where the function reaches a relative maximum or minimum.