3. Partial Derivatives

Maxima, Minima, And Saddle Points — Quiz

Test your understanding of maxima, minima, and saddle points with 5 practice questions.

Practice Questions

Question 1

Consider the function $f(x,y) = x^3 - 3xy + y^3$. What is the correct classification of the critical point at $(0,0)$?

Question 2

For the function $f(x,y) = x^4 + y^4 - 4xy$, what are the coordinates of the critical points?

Question 3

Given the function $f(x,y) = x^2 + y^2 - 2xy + 3$, what is the nature of the critical point at $(0,0)$?

Question 4

Find the critical points of the function $f(x,y) = x^2y + y^2 - 3x - 2y$. Which of the following is a correct critical point?

Question 5

Consider the function $f(x,y) = x^3 - 3xy + y^3$. What is the value of the discriminant $D$ at the critical point $(1,1)$?