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 are the critical points of this function?

Question 2

For the function $g(x,y) = x^2 + 4y^2 - 4xy + 2$, what is the nature of the critical point at $(0,0)$?

Question 3

Which of the following functions has a local maximum at $(0,0)$?

Question 4

Consider the function $f(x,y) = x^4 + y^4 - 4xy$. Find the critical points and classify the point $(0,0)$.

Question 5

For the function $f(x,y) = x^2y - \frac{y^3}{3}$, what is the classification of the critical point at $(0,0)$?