Calculus BC Semester 1Final Exam Review

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What is the definition of a critical number in calculus?

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A critical number of a function is a number in the domain of the function where the derivative is either zero or undefined.

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How do you find the acceleration of an object given its position function x(t)?

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To find the acceleration, take the second derivative of the position function x(t) with respect to time t.

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What is the purpose of Riemann sums in numerical integration?

Back

Riemann sums are used to approximate the area under a curve by dividing it into rectangles and summing their areas.

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Back

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What is the quotient rule in calculus?

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What is the second derivative test used for?

Back

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

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What does it mean for a function to be increasing or decreasing?

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A function is increasing on an interval if its derivative is positive on that interval, and decreasing if its derivative is negative.

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What is the Fundamental Theorem of Calculus?

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How do you find the area under a curve using integration?

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

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The first derivative indicates the slope of the tangent line to the graph of the function; where it is positive, the function is increasing, and where it is negative, the function is decreasing.