Math Analysis Partial Derivatives Lagrange Multipliers Online Lesson

Objective: Today you are going to participate in an online lesson created to teach you about Lagrange Multipliers.  At the end of this class you will be able to:
 
  • Use Lagrange Multipliers to maximize or minimize a function subject to constraints on the variables.
Directions: Perform the following tasks in order.  Read all directions carefully.  Make sure to pay close attention during the videos taking notes and doing the example problems along with the instructors (Its okay to pause the video if it is going to fast to do so!).  If you have any questions, check and make sure that the answer has not been given in the directions.  If you have done this and your answer has not been given, ask Mr. Wood!  
 
1.Watch the video on Lagrange Multipliers: Lagrange Multipliers Overview.

If you still need additional understanding of the concept, you can look at the following introduction also:

Intro to Lagrange Multipliers

 



2. Watch the following example of Lagrange Multipliers: Lagrange Multipliers.

The following example is using Lagrange Multipliers for a function of three variables:

Three Variable Lagrange Example

 


3. Complete the following example using Lagrange Multipliers.  You have done this using the other method already!
 
A rectangular box without a lid is to be made from 12 square meters of cardboard.  Find the maximum value of such a box.


Check your work with Mr. Wood when complete.

 



4.Complete the following example using Lagrange Multipliers.  
 
Find the extreme values of the function:
on the circle with radius 1 and centered at the origin.

Check your work with Mr. Wood when complete.

 



  
5.Complete the following example using Lagrange Multipliers.  
 
Find the points on
that are closest to and farthest from (3, 1, -1).

Check your work with Mr. Wood when complete.

 


 
Conclusion: Congratulations! You have completed the online lesson for today!