The point is a critical point for the multivariable function if both partial derivatives are 0 at the same time.
In other words,
and
mathstat.slu.edu/~may/ExcelCalculus/external/Examples/Section-6-3-Examples.xlsx
p | |||||
A | 0 | 0 | 0 | 0 | 1 |
B | 0 | 1 | 3 | 2 | 4 |
C | 1 | 0 | 0 | 2 | 3 |
D | 0 | 0 | 1 | 2 | 0 |
E | 0 | 0 | -1 | 2 | 3 |
F | 0 | 0 | -3 | 1 | -2 |
G | 0 | 0 | 3 | 3 | 3 |
p | Discriminant | Classification | |||||
A | 0 | 0 | 0 | 0 | 1 | 0 | Not enough information |
B | 0 | 1 | 3 | 2 | 4 | 8 | Not a critical point |
C | 1 | 0 | 0 | 2 | 3 | -4 | Not a critical point |
D | 0 | 0 | 1 | 2 | 0 | -4 | Saddle point |
E | 0 | 0 | -1 | 2 | 3 | -7 | Saddle point |
F | 0 | 0 | -3 | 1 | -2 | 5 | Maximum |
G | 0 | 0 | 3 | 3 | 3 | 0 | Not enough information |
p | |||||
A | 1 | 2 | 3 | 4 | 5 |
B | 0 | 0 | 0 | 0 | 0 |
C | 0 | 1 | 2 | 5 | 3 |
D | 0 | 0 | 2 | 2 | 2 |
E | 0 | 0 | 1 | 2 | 3 |
F | 0 | 0 | 0 | 1 | 0 |
G | 0 | 0 | 0 | -1 | 0 |
p | Classification | ||||||
A | 1 | 2 | 3 | 4 | 5 | -1 | Not Critical |
B | 0 | 0 | 0 | 0 | 0 | 0 | Not Enough Info |
C | 0 | 1 | 2 | 5 | 3 | -19 | Not Critical |
D | 0 | 0 | 2 | 2 | 2 | 0 | Not Enough Info |
E | 0 | 0 | 1 | 2 | 3 | -1 | Saddle Point |
F | 0 | 0 | 0 | 1 | 0 | 0 | Not Enough Info |
G | 0 | 0 | 0 | -1 | 0 | 0 | Not Enough Info |
p | |||||
A | 1 | 2 | 3 | 4 | 5 |
B | 0 | 0 | 0 | 0 | 0 |
C | 0 | 1 | 2 | 5 | 3 |
D | 0 | 0 | 2 | 2 | 2 |
E | 0 | 0 | 1 | 2 | 3 |
F | 0 | 0 | 0 | 1 | 0 |
G | 0 | 0 | 0 | -1 | 0 |