1.0
0.5
0.0
2
-0.5
0
-2
0
-2
2
Figure 1. Graph of f (x, y) =
x2
8
−
y2
12
Figure 2. Gradient vector field for f (x, y) =
1
x2
8
−
y2
12
2
0.8
0.6
1.0
0.4
0.2
0.0
0.0
0.5
0.5
1.0
0.0
Figure 3. Graph of f (x, y) = sin(xy)
Figure 4. Gradient vector field for f (x, y) = sin(xy)
3
100
50
10
0
5
-50
-100
-10
0
-5
-5
0
5
10 -10
Figure 5. Graph of f (x, y) = 100 − x2 − y 2
Figure 6. Gradient vector field for f (x, y) = 100 − x2 − y 2
4
Figure 7. Gradient vector field of f (x, y, z) = sin(xyz)