Unit 5 Check 1 - theorems

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Mathematics
•
10th Grade - University
•
Hard
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1.
FLASHCARD QUESTION
Front
What is Rolle's Theorem?
Back
Rolle's Theorem states that if a function is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and F(a) = F(b), then there exists at least one c in (a, b) such that F'(c) = 0.
2.
FLASHCARD QUESTION
Front
What are the conditions for the Mean Value Theorem?
Back
The Mean Value Theorem requires that a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b).
3.
FLASHCARD QUESTION
Front
What does it mean for a function to have a critical value?
Back
A critical value of a function occurs where its derivative is zero or undefined, indicating potential local maxima, minima, or points of inflection.
4.
FLASHCARD QUESTION
Front
How do you find critical values of a function?
Back
To find critical values, take the derivative of the function, set it equal to zero, and solve for x. Also, check where the derivative does not exist.
5.
FLASHCARD QUESTION
Front
What is the significance of a zero in a function's interval?
Back
A zero in a function's interval indicates that the function crosses the x-axis, which can be found using the Intermediate Value Theorem if the function is continuous.
Tags
CCSS.HSA.APR.B.3
6.
FLASHCARD QUESTION
Front
What is the Intermediate Value Theorem?
Back
The Intermediate Value Theorem states that if a function is continuous on [a, b] and takes on values F(a) and F(b), then it takes on every value between F(a) and F(b) at least once.
7.
FLASHCARD QUESTION
Front
What is the formula for the Mean Value Theorem?
Back
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