This is a question on multivariable calculus. I am given a contour map (provided in the image link) and asked to solve for the smallest angle that yields a zero for the directional vector. Here is the exact problem:
"A contour plot for z=f(x,y) is illustrated with normal vector in orange. Using the interactive controls, determine the smallest positive angle for which the directional derivative is zero at the point (−2/3,−2/3)."
I would greatly appreciate any help.
Hint
remember that the contour curves are curves with constant $z$, so the the change of $z$ in the direction tangent to a contour curve is null.