Local Max, Min or Saddle: 2nd Derivative Test
GROUP MEMBERS:
1. _____________________________
2. ______________________________
3. ______________________________
4. ______________________________
Problem: To use the 2nd derivative test to determine local maximum, minimum or saddle.
Directions: Each person will do an example on her own. When everyone has done their example, they will share it with the group. For your function, find the critical points and then determine if the critical point is a local max or min or saddle using the 2nd derivative test.
Person 1: f(x,y) = 3x2 + 4 y2.
Person 2: f(x,y) = 3x2 - 4 y2.
Person 3: f(x,y) = -3x2 - 4 y2.
Person 4: f(x,y) = -3x2 + 4 y2.
After you have discussed these results with each other, do the following examples.
Person 1: g(x,y) = 3x4 + 4 y4.
Person 2: g(x,y) = 3x4 - 4 y4.
Person 3: g(x,y) = -3x4 - 4 y4.
Person 4: g(x,y) = -3x4 + 4 y4.