True or False? Brief explanation. а. If f : R? → R is differentiable at all points, and f has a local minimum at the point A, then for any unit vector u, we must have Duf(A) > 0. b. Let S be a...

Extracted text: True or False? Brief explanation. а. If f : R? → R is differentiable at all points, and f has a local minimum at the point A, then for any unit vector u, we must have Duf(A) > 0. b. Let S be a bounded, oriented surface in R³. If F is a vector field in R³ and ||F|| > 0 at all points of S, then Sg F · dS will be positive.