3. Partial Derivatives

Lagrange Multipliers — Quiz

Test your understanding of lagrange multipliers with 5 practice questions.

Practice Questions

Question 1

What is the primary purpose of using Lagrange multipliers in calculus?

Question 2

Given a function $f(x, y) = x^2 + y^2$ and a constraint $g(x, y) = x + y - 1 = 0$, what is the correct system of equations to solve using Lagrange multipliers?

Question 3

Consider the function $f(x, y) = xy$ subject to the constraint $x^2 + y^2 = 1$. What are the critical points found using Lagrange multipliers?

Question 4

Which condition must hold at the solution point when using the method of Lagrange multipliers for a single constraint?

Question 5

Find the minimum value of $f(x, y) = x^2 + y^2$ subject to $x + 2y = 4$ using Lagrange multipliers.