Question

Please help me determine whether the following statement is true or false and explain your reasoning. If the line y=2 is a contour of f(x,y) through (4,2) then fx(4,2)=0.

Answer 1

After some time of researching, I think I understand this problem, although a second opinion may be good

We are saying that the line y=2 is a contour of f(x,y), so f(x,2) = k along the line. If we take the partial derivative of both sides for f_x, then f_x (x,2) = d/dx k = 0. Thus, this would be true for x=4.

My main uncertainty is just whether I am understanding the definition of the contour line correctly in this situation: a contour line is a graph of some particular value of z=f(x,y).