AP Calculus AB Final Review Check

Front

What is the definition of a limit in calculus?

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A limit is a value that a function approaches as the input approaches some value.

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What does it mean for a function to be continuous at a point?

Back

A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point.

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What is the derivative of a function?

Back

The derivative of a function represents the rate of change of the function with respect to its variable.

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How do you find the critical points of a function?

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Critical points are found by setting the derivative of the function equal to zero and solving for the variable.

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What is the Mean Value Theorem?

Back

The Mean Value Theorem states that if a function is continuous on a closed interval and differentiable on the open interval, then there exists at least one point where the derivative equals the average rate of change over that interval.

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What is the relationship between a function and its first derivative?

Back

The first derivative of a function indicates the slope of the tangent line to the function's graph, showing where the function is increasing or decreasing.

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What is the second derivative test used for?

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The second derivative test is used to determine the concavity of a function and to classify critical points as local maxima, local minima, or points of inflection.

Front

What is the formula for the derivative of a trigonometric function, specifically sine?

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The derivative of sin(x) is cos(x).

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Back

The derivative of tan(x) is sec^2(x).

Front

What is the Fundamental Theorem of Calculus?

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