6. Optimization

Critical Points — Quiz

Test your understanding of critical points with 5 practice questions.

Practice Questions

Question 1

For a differentiable function $f(x,y)$, which condition is necessary at a critical point?

Question 2

Find the critical point of $f(x,y)=x^2+y^2$.

Question 3

Find the critical point of $f(x,y)=x^2-4x+y^2+2y$.

Question 4

How many critical points does $f(x,y)=x^3-3x+y^2$ have?

Question 5

Which point is a critical point of $f(x,y)=x^2+xy+y^2$?