MVT, IVT, EVT

MVT, IVT, EVT

Assessment

Flashcard

Mathematics

12th Grade

Practice Problem

Hard

Created by

Wayground Content

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Mean Value Theorem (MVT)?

Back

The MVT 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 point c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).

2.

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], and N is any number between f(a) and f(b), then there exists at least one point c in (a, b) such that f(c) = N.

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

Can the MVT be applied to the function f(x) = (-x^2 + 9)/(4x) on [1,3]?

Back

Yes, the MVT can be applied because the function is continuous and differentiable on the interval.

5.

FLASHCARD QUESTION

Front

Find all values of c that satisfy the MVT for f(x) = -x^2 + 8x - 17 on [2,6].

Back

c = 4.

6.

FLASHCARD QUESTION

Front

Find the value of c guaranteed by the IVT for f(x) = x^2 + x - 1 on [0,5] where f(c) = 11.

Back

c = 3.

7.

FLASHCARD QUESTION

Front

If f(x) is continuous on the interval [-2, 5] and f(-2) = 5 and f(5) = -2, what theorem applies?

Back

IVT.

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