

Lagrange Multipliers and Optimization
Interactive Video
•
Mathematics
•
11th Grade - University
•
Practice Problem
•
Hard
+2
Standards-aligned
Jackson Turner
FREE Resource
Standards-aligned
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the primary goal when using Lagrange multipliers in this example?
To determine the gradient of a function.
To solve a system of linear equations.
To find the minimum value of a function.
To find the maximum value of a function.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the constraint equation in this example?
x + y + z = 49
f(x, y, z) = 0
2x - 3y - 4z = 49
g(x, y, z) = 0
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the gradient of f related to the gradient of g in this method?
The gradient of f is equal to lambda times the gradient of g.
The gradient of f is twice the gradient of g.
The gradient of f is half the gradient of g.
The gradient of f is equal to the gradient of g.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the partial derivative of f with respect to x?
2x
4x
6x
x
Tags
CCSS.8.EE.C.8B
CCSS.HSA.REI.C.6
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the value of x in terms of lambda after solving the first equation?
x = 3 lambda
x = 1/2 lambda
x = 2 lambda
x = lambda
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the next step after expressing x, y, and z in terms of lambda?
Find the maximum value of the function.
Substitute x, y, and z back into the original function.
Substitute x, y, and z into the constraint equation.
Solve for x, y, and z directly.
Tags
CCSS.HSA.REI.A.2
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the common denominator used to solve for lambda?
5
4
3
6
Tags
CCSS.7.EE.B.4A
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