MVT, EVT, IVT (SPHS)

MVT, EVT, IVT (SPHS)

Assessment

Flashcard

Mathematics

11th - 12th Grade

Hard

CCSS
HSA.APR.B.3, HSF-IF.C.7B

Standards-aligned

Created by

Wayground Content

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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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