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Questions and Answers
What does the mean value theorem state?
What does the mean value theorem state?
- For a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints. (correct)
- For a given planar arc between two endpoints, the tangent to the arc is never parallel to the secant through its endpoints.
- For a given planar arc between two endpoints, the tangent to the arc is always parallel to the secant through its endpoints.
- For a given planar arc between two endpoints, the tangent to the arc is perpendicular to the secant through its endpoints.
In which interval does the mean value theorem hold true?
In which interval does the mean value theorem hold true?
- (a, b) (correct)
- [a, b]
- (a, b]
- [a, b)
What is the formula representing the mean value theorem?
What is the formula representing the mean value theorem?
- $f'(c) = \frac{b - a}{f(b) - f(a)}$
- $f'(c) = \frac{f(b) + f(a)}{b + a}$
- $f'(c) = \frac{b + a}{f(b) + f(a)}$
- $f'(c) = \frac{f(b) - f(a)}{b - a}$ (correct)
Who first described a special case of the mean value theorem for inverse interpolation of the sine?
Who first described a special case of the mean value theorem for inverse interpolation of the sine?
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What type of function does the mean value theorem require to be on the closed interval [a, b]?
What type of function does the mean value theorem require to be on the closed interval [a, b]?
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