2D Constrained Optimization: build a function graph and a restriction graph; find the location of optimal points and determine whether this is maximum or minimum applying the Lagrange method. \(f(x_1, x_2) = x_1^2 - x_1x_2^2\) \(x_1 - x_2 + 4 = 0\)
Added by Danielle V.
Close
Step 1
To build the function graph, we need to plot the points (x1, x2) that satisfy the equation f(x1, x2) = x2 - x1x2. However, since we have a constraint equation as well, we need to consider only the points that satisfy both the function and the constraint. Show more…
Show all steps
Your feedback will help us improve your experience
Ashar Tanveer and 69 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Use Lagrange multipliers to find any extrema of the function subject to the constraint x^2 + y^2 ≤ 1. f(x, y) = e^(-xy/4) minimum f( ) = (smaller x-value) minimum f( ) = (larger x-value) maximum f( ) = (smaller x-value) maximum f( ) = (larger x-value)
Adi S.
Use Lagrange multipliers to find the maximum and minimum values of $f$ subject to the constraint $g(x, y)=0 .$ $$ f(x, y)=x^{2}+4 y^{3}, g(x, y)=x^{2}+2 y^{2}-2=0 $$
Directional Derivatives, Gradients, and Extrema
Lagrange Multipliers
Use Lagrange multipliers to find the maximum and minimum values of $f$ (when they exist) subject to the given constraint. $f(x, y)=x+2 y$ subject to $x^{2}+y^{2}=4$
Functions of Several Variables
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Watch the video solution with this free unlock.
EMAIL
PASSWORD