
Understanding Existence Theorems and Their Applications

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard
Standards-aligned

Aiden Montgomery
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main focus of the problem introduced in the video?
Determining the existence of a maximum value over an interval
Identifying the roots of a polynomial
Finding the derivative of a function
Calculating the integral of a function
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which theorem is likely being discussed when talking about the existence of a maximum or minimum value over an interval?
Fundamental Theorem of Calculus
Mean Value Theorem
Extreme Value Theorem
Pythagorean Theorem
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a necessary condition to apply the Extreme Value Theorem?
The function must be continuous over the closed interval
The function must be differentiable
The function must be increasing
The function must be decreasing
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the condition 'f is increasing in the open interval from two to three and decreasing on the open interval from three to five' ruled out?
It guarantees a maximum value
It implies the function is constant
It ensures differentiability
It does not ensure continuity over the interval
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does differentiability imply about a function?
The function is always decreasing
The function is always increasing
The function is constant
The function is continuous
Tags
CCSS.HSF.IF.A.2
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the new problem, what is Clyde trying to determine?
If h(x) is equal to 10
If h(x) is equal to 5
If h(x) is equal to negative 2
If h(x) is equal to 0
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What mistake did Clyde make in his solution?
He applied the Extreme Value Theorem
He applied the Fundamental Theorem of Calculus
He applied the Mean Value Theorem
He applied the Pythagorean Theorem
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