How would I compute the possible values of a gradient vector, without knowing $f(x,y)$? I have the level curve $y = 9x+6$ and $|\nabla f(3,14)|$ = 10.
I think I should take the perpendicular slope of the level curve, giving me $\left<-1, 9\right>$. So this would give me the direction. I also have the length of the gradient, 10. I'm not entirely sure how to tie the two together to get the gradient vector.