
Understanding the Mean Value Theorem
Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
Aiden Montgomery
FREE Resource
Standards-aligned
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is Raphael's claim regarding the mean value theorem?
The function g has no derivative.
The function g is continuous everywhere.
The function g is always increasing.
There is a number c where g'(c) equals the average rate of change.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the average rate of change between two points on a function defined?
As the product of the function values at those points.
As the difference in y-values divided by the difference in x-values.
As the integral of the function between those points.
As the sum of the function values at those points.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the mean value theorem require about a function on a closed interval?
The function must be differentiable and continuous.
The function must be constant.
The function must be increasing.
The function must be decreasing.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the mean value theorem in calculus?
It proves the function is always increasing.
It ensures a point where the derivative equals the average rate of change.
It guarantees a point where the function is zero.
It shows the function is always continuous.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which condition is NOT sufficient for applying the mean value theorem?
The function is continuous over the closed interval.
The function is differentiable at a single point.
The function is differentiable over the open interval.
The function is continuous at the endpoints.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is it important to establish conditions before applying the mean value theorem?
To verify the function is quadratic.
To confirm the function is differentiable and continuous.
To check if the function is periodic.
To ensure the function is linear.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does differentiability imply about a function?
The function is continuous.
The function is constant.
The function is increasing.
The function is decreasing.
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