Lagrange Multipliers and Extrema
Interactive Video
•
Mathematics
•
11th Grade - University
•
Practice Problem
•
Hard
+1
Standards-aligned
Mia Campbell
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the constraint equation used in the problem?
x^2 + y^2 = 0
x^2 - y^2 = 0
x^2 - y^2 = 81
x^2 + y^2 = 81
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the form of the constraint equation g(x, y) used in Lagrange multipliers?
g(x, y) = x^2 - y^2 - 81
g(x, y) = x^2 - y^2 + 81
g(x, y) = x^2 + y^2 - 81
g(x, y) = x^2 + y^2 + 81
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the partial derivative of f with respect to x?
-2x + 5
2x + 5
-2y + 5
2y + 5
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you solve for x in the first equation?
Add 2x to both sides and divide by lambda
Subtract 2x from both sides and multiply by lambda
Add 2x to both sides and factor out 2x
Subtract 2x from both sides and factor out 2x
Tags
CCSS.6.EE.C.9
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the relationship between x and y found in the solution?
x = y/2
x = y
x = -y
x = 2y
Tags
CCSS.HSA.REI.C.7
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What are the possible values for x and y after solving the equations?
x = ±√2, y = ±√2
x = ±9, y = ±9
x = ±2, y = ±2
x = ±9/√2, y = ±9/√2
Tags
CCSS.HSF.IF.A.2
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the approximate function value when both x and y are positive?
-21.3604
148.6396
-148.6396
21.3604
Tags
CCSS.HSF.IF.A.2
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