Mean Value Theorem
Flashcard
•
Mathematics
•
11th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the Mean Value Theorem?
Back
The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).
2.
FLASHCARD QUESTION
Front
What does the Mean Value Theorem imply about the slope of a function?
Back
It implies that there is at least one point in the interval where the instantaneous rate of change (slope of the tangent) equals the average rate of change over the interval.
3.
FLASHCARD QUESTION
Front
How do you find the average rate of change of a function over an interval?
Back
The average rate of change of a function f(x) over the interval [a, b] is calculated as (f(b) - f(a)) / (b - a).
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
4.
FLASHCARD QUESTION
Front
What is the derivative of f(x) = 12√(x)?
Back
f'(x) = 6 / √(x).
5.
FLASHCARD QUESTION
Front
What is the derivative of f(x) = x² + 5x + 5?
Back
f'(x) = 2x + 5.
6.
FLASHCARD QUESTION
Front
What is the derivative of f(x) = (x-4)/(x+1)?
Back
f'(x) = 5 / (x+1)².
7.
FLASHCARD QUESTION
Front
What is the significance of the derivative in the context of the Mean Value Theorem?
Back
The derivative represents the instantaneous rate of change of the function, which is compared to the average rate of change over an interval.
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