Let S be a surface defined by xy + z^3 = 2 in a neighborhood of the point (1,1,1). Let f = f(x,y,z) be of Class C1. Denote by f|s the restriction of f to S. Suppose that the point (1,1,1) is a local minimum of f\s. If: zf(1,1,1)=1 , find xf(1,1,1) and yf(1,1,1) .

I also don't understand the classification C1, I can't find anything in my textbook about these. Could you walk me through the solution, as well as point me in the right direction for learning these classifications. Thank you