
Understanding Extrema and Lagrange Multipliers
Interactive Video
•
Mathematics
•
11th Grade - University
•
Practice Problem
•
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 first step in finding the absolute extrema of a function within a bounded region?
Find the critical points and evaluate the function at these points.
Use the method of Lagrange multipliers.
Calculate the second derivative of the function.
Graph the function and identify the highest and lowest points.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What do you need to calculate to find the critical points of a function?
The gradient of the function.
The integral of the function.
The first order partial derivatives.
The second derivative of the function.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why does the function f(x, y) = 4x + 5y have no critical points in the bounded region?
Because the function is not differentiable.
Because the function is linear.
Because the partial derivatives are constants and never zero.
Because the partial derivatives are zero.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of using Lagrange multipliers in finding extrema?
To approximate the function values.
To find extrema on the boundary of the region.
To solve the function using calculus one techniques.
To find critical points inside the region.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What condition must be met for the gradients of f and g in the Lagrange multipliers method?
They must be zero.
They must be parallel.
They must be equal.
They must be perpendicular.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of Lagrange multipliers, what does it mean when the level curves of f and g are tangent?
The gradients are perpendicular.
The gradients are parallel.
The function has no extrema.
The function is undefined.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the constraint equation used in the Lagrange multipliers method for this problem?
x^2 + y^2 = 4
x^2 + y^2 = 16
4x + 5y = 0
x + y = 0
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