Consider the function ϕ(x,y) =
x2 + y2.
- (1 pt) Find the gradient field for
ϕ(x,y).
- (1 pt) Describe the level cuves of
ϕ(x,y).
- (2 pts) Sketch some level curves of ϕ(x,y) as
well the gradient field.
- (1 pt) What do you notice about the relationship between the
level curves and the gradient field?