3. Partial Derivatives

Lagrange Multipliers — Quiz

Test your understanding of lagrange multipliers with 5 practice questions.

Practice Questions

Question 1

What is the primary goal of the Lagrange multipliers method in multivariable calculus?

Question 2

Which equation correctly represents the condition for applying the Lagrange multipliers method for a function $f(x, y)$ subject to a constraint $g(x, y) = 0$?

Question 3

Suppose we want to find the extrema of $f(x, y) = x^2 + y^2$ subject to the constraint $x + y = 1$. What system of equations results from applying Lagrange multipliers?

Question 4

Find the critical points of $f(x, y) = x^2 + 4y^2$ subject to the constraint $x + 2y = 6$ using Lagrange multipliers. What are the values of $x$ and $y$ at the critical point?

Question 5

Consider the function $f(x, y, z) = x^2 + y^2 + z^2$ subject to the constraint $x + y + z = 1$. Which of the following is the correct system of equations for the Lagrange multiplier approach?