
Understanding Relative Extrema in Functions of Two Variables

Interactive Video
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Mathematics
•
11th Grade - University
•
Hard

Olivia Brooks
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a saddle point in the context of functions of two variables?
A point where the function is undefined
A point where the function has a relative minimum
A point that is neither a relative maximum nor minimum
A point where the function has a relative maximum
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which condition must be met for a function to have a relative minimum at a point (a, b)?
f(a, b) > f(x, y) for all (x, y) in the region
f(a, b) < f(x, y) for all (x, y) in the region
f(a, b) ≤ f(x, y) in some region containing (a, b)
f(a, b) = f(x, y) for all (x, y) in the region
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in determining the relative extrema of a function of two variables?
Calculate the second-order partial derivatives
Find the critical numbers where the first-order partial derivatives are zero or do not exist
Graph the function
Solve the function for zero
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the first example, what is the value of the second-order partial derivative with respect to x?
Negative two
Positive two
Negative ten
Zero
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the value of d in the first example, and what does it indicate?
d = 0, indicating the test is inconclusive
d = -20, indicating a saddle point
d = 20, indicating a relative maximum
d = 20, indicating a relative minimum
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the second example, what are the critical points found?
(0, 0) and (1, 1)
(2, 2) and (3, 3)
(1, 0) and (0, 1)
(4, -1) and (1, 1)
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does a negative value of d indicate in the context of relative extrema?
A relative minimum
The test is inconclusive
A relative maximum
A saddle point
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