Question

Is the gradient of a function basically like the slope field.
Also what is a conservative vector field. I know the definition but I'm having trouble visualizing it

Thanks

Answer 1

1, yes
2. a "conservative" vector field is one in which if one goes from point A to point B, the change in potential from A to B does not depend on the path taken.
Consider from the top of the Mountain to some point B on the bottom, the change in potential energy from the top to point B does not depend on how you got down the mountain.