6. Optimization

Second Derivative Test — Quiz

Test your understanding of second derivative test with 5 practice questions.

Practice Questions

Question 1

In the second derivative test for a function $f(x,y)$, what is the quantity $D$ evaluated at a critical point?

Question 2

If at a critical point $D>0$ and $f_{xx}>0$, what does the second derivative test say?

Question 3

If at a critical point $D>0$ and $f_{xx}<0$, what does the second derivative test conclude?

Question 4

If at a critical point $D<0$, what does the second derivative test conclude?

Question 5

Let $f(x,y)=x^2+y^2$. What type of point is $(0,0)$ according to the second derivative test?