Lagrange Multipliers and Constraints

Lagrange Multipliers and Constraints

Assessment

Interactive Video

Created by

Mia Campbell

Mathematics

11th Grade - University

Hard

The video tutorial explains how to use the method of Lagrange multipliers to find the minimum value of a function subject to a constraint. It involves setting up a system of equations using partial derivatives, solving for lambda, and calculating the minimum point. The solution is verified graphically, confirming the minimum value under the given constraint.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the primary goal when using the method of Lagrange multipliers?

To solve linear equations

To find the minimum or maximum value of a function subject to a constraint

To find the maximum value of a function without constraints

To determine the derivative of a function

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the form of the constraint equation in the method of Lagrange multipliers?

f(x, y) = 0

k(x, y) = 0

g(x, y) = 0

h(x, y) = 0

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you find the partial derivative of f with respect to x?

Differentiate f with respect to x, treating x as a constant

Differentiate f with respect to y, treating x as a constant

Differentiate f with respect to x, treating y as a constant

Differentiate f with respect to both x and y

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of lambda when solving the system of equations?

20/17

40/17

80/17

17/40

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the x-coordinate of the point that represents the minimum value?

40/17

20/17

80/17

17/20

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the y-coordinate of the point that represents the minimum value?

20/17

17/80

40/17

80/17

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the minimum function value found in the problem?

400/17

417

17/400

17/417

8.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How can you verify whether the point found is a minimum or maximum?

By checking the first order partial derivatives

By assuming based on the question

By finding the second order partial derivatives and applying the second partials test

By solving the constraint equation again

9.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the red point on the graph represent?

An average function value

A point of inflection

A minimum function value

A maximum function value

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the constraint equation used in this problem?

x + 4y = 20

x - 4y = 0

x - 4y = 20

x + 4y = 0

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