Chp 7: PD 3 Flashcards
1
Q
Linear approximation/ tangent plane formula
A
Z(x,y) = z node + fx(x node, y node) (dx) + fy(x node, y node) (dy)
2
Q
d^2y/dx^2 is more than 0
A
Minimum point
3
Q
d^2y/dx^2 is less than 0
A
Maximum point
4
Q
d^2y/dx^2 = 0
A
Saddle point
5
Q
Relative maximum
A
Highest point at a region
6
Q
Relative minimum
A
Lowest point at a region
7
Q
Absolute maximum
A
Highest point in the whole domain
8
Q
Absolute minimum
A
lowest point in the whole domain
9
Q
Extreme value theorem
A
f(x,y) has a absolute minimum and maximum if it is continuous and bounded in a region.
10
Q
Finding absolute extrema
A
- Find the critical points
- Find all the boundary points
- Evaluate the largest values (absolute maximum) and the smallest values (absolute minimum).
