Gradients And Directional Derivatives 2

Question 1

If the f(x,y) is differentiable at (a,b) then what is grad(f(a,b))

Answer 1

If the f(x,y) is differentiable at (a,b) then grad(f(a,b)) is a vector normal to level curve (contour) of f(x,y) at (a,b)

Question 2

What direction is grad(f(a,b)) in and what happens if u is a unit vector

Answer 2

Grad(f(a,b)) is in direction of maximal increase of f at (a,b) and if u is a unit vector in the direction of grad(f(a,b)) then Duf = norm(grad(f))