REVIEW 2.1 DEFINITION OF DERIVATIVES

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What is the definition of a derivative?

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The derivative of a function at a point measures the rate at which the function's value changes as its input changes. It is defined as the limit of the average rate of change of the function as the interval approaches zero.

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What does it mean if a function's derivative is negative?

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If a function's derivative is negative, it indicates that the function is decreasing at that point.

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What does DNE stand for in calculus?

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DNE stands for 'Does Not Exist', indicating that the derivative is not defined at that point.

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What is the significance of a vertical tangent line at a point?

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A vertical tangent line at a point indicates that the derivative does not exist at that point, often due to a sharp turn or cusp in the graph.

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What is the relationship between a function's increasing/decreasing behavior and its derivative?

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A function is increasing where its derivative is positive and decreasing where its derivative is negative.

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What is the geometric interpretation of a derivative?

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The derivative at a point represents the slope of the tangent line to the graph of the function at that point.