Let P be a point in the domain of a smooth function f of three variables.

(a) Find the gradient of f at P if all of the following is known:

• f(P)=3 ;
• The plane x+2y-z=0 is tangent to the level surface of f going through P;
• The first coordinate of f(P) is positive.

(b) Let r(t) = be a smooth curve such that r(0) = P and r'(0) = <1,1,0>. Find dtd (f(r(t)) at t = 0. [Here, f is the same function and P is the same point as in part (a)].