Lagrange Multipliers and Maximum Values

Lagrange Multipliers and Maximum Values

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

CCSS
8.EE.C.8B, HSA.REI.C.6

Standards-aligned

Created by

Mia Campbell

FREE Resource

Standards-aligned

CCSS.8.EE.C.8B
,
CCSS.HSA.REI.C.6
The video tutorial explains how to use Lagrange multipliers to find the maximum value of a function subject to a constraint. It covers setting up the problem, solving the system of equations, and verifying the result graphically. The tutorial concludes with a summary of the findings.

Read more

10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the primary goal when using Lagrange multipliers in this problem?

To determine the gradient of a function.

To find the minimum value of a function.

To find the maximum value of a function.

To solve a system of linear equations.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the constraint equation in this problem?

x + 5y = 0

x + 5y = 64

x - 5y = 64

x + y = 64

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

According to Lagrange's theorem, when does a maximum or minimum occur?

When the gradients of f and g are parallel.

When the gradients of f and g are zero.

When the gradients of f and g are perpendicular.

When the gradients of f and g are equal.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the partial derivative of f with respect to x?

x

y

1

0

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the partial derivative of g with respect to y?

x

5

y

0

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

32/5

64/5

64/10

32/10

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the values of x and y at the maximum point?

x = 64, y = 64/5

x = 64, y = 32/5

x = 32, y = 32/5

x = 32, y = 64/5

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Google

Continue with Google

Email

Continue with Email

Classlink

Continue with Classlink

Clever

Continue with Clever

or continue with

Microsoft

Microsoft

Apple

Apple

Others

Others

Already have an account?