MVT, EVT, IVT (SPHS)
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 Intermediate Value Theorem (IVT)?
Back
The IVT states that if a function is continuous on a closed interval [a, b], then for any value L between f(a) and f(b), there exists at least one c in (a, b) such that f(c) = L.
2.
FLASHCARD QUESTION
Front
What is the Mean Value Theorem (MVT)?
Back
The MVT states that if a function is continuous on [a, b] and differentiable on (a, b), then there exists at least one c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).
3.
FLASHCARD QUESTION
Front
What is the Extreme Value Theorem (EVT)?
Back
The EVT states that if a function is continuous on a closed interval [a, b], then it must attain a maximum and a minimum value at least once in that interval.
4.
FLASHCARD QUESTION
Front
When does the IVT apply?
Back
The IVT applies when a function is continuous on a closed interval [a, b] and the values of the function at the endpoints f(a) and f(b) are different.
Tags
CCSS.HSA.APR.B.3
5.
FLASHCARD QUESTION
Front
What does it mean for a function to be continuous?
Back
A function is continuous if there are no breaks, jumps, or holes in its graph, meaning it can be drawn without lifting the pencil.
Tags
CCSS.HSF-IF.C.7B
6.
FLASHCARD QUESTION
Front
Provide an example of a function that satisfies the conditions of the IVT.
Back
f(x) = x^2 is continuous on [1, 4]. Since f(1) = 1 and f(4) = 16, the IVT guarantees that there is a c in (1, 4) such that f(c) = 10.
7.
FLASHCARD QUESTION
Front
What is the significance of the derivative in the MVT?
Back
The derivative f'(c) represents the instantaneous rate of change of the function at point c, which equals the average rate of change over the interval [a, b].
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