6. Optimization

Lagrange Multipliers — Quiz

Test your understanding of lagrange multipliers with 5 practice questions.

Practice Questions

Question 1

Which equation is the key condition for a constrained extremum of $f(x,y)$ subject to $g(x,y)=c$?

Question 2

At a constrained extremum with one smooth constraint, what is the relationship between $\nabla f$ and $\nabla g$?

Question 3

What point minimizes $f(x,y)=x^2+y^2$ subject to $x+y=6$?

Question 4

What is the maximum value of $f(x,y)=xy$ subject to $x+y=10$?

Question 5

For $f(x,y)=x^2+y^2$ subject to $x+y=6$, what is the value of $\lambda$ at the minimum point?