I think the author’s figure and my figure is same.

Since a vector has no position, author indicated a vector field in graphical form by placing the vector f(x,y) with its tail at (x,y). But the octave did reverse. Octave indicated a vector field in graphical form by placing the vector f(x,y) with its face at (x,y).

I get the same quiver field as you. f(1,0) = <-1/sqrt(5), 0>, whereas his arrows indicate a postitive x-direction at (1,0). therefore the plot shown must be some other scaled version of the simple quiver field (his answer shows -f(x,y) as you’ve defined it). note that it is fairly common to define a potential vector field as -grad(f)