(*******
Find the equation of the tangent plane and the normal line to the graph of f(x,y) = (x^2-y^3)/6 at point (3, 2, 1/6)
*****)

F =z- ((x^2)- (y^3))/6;
grad[x_,y_,z_] = {D[F,x],D[F,y],D[F,z]}

p = {3,2,1/6};
n = grad[3,2,1/6]
n.{x,y,z} == n.p

(***
Normal line:
**)
r[t_] = p + t n
graph=Plot3D[((x^2)- (y^3))/6,{x,2,4},{y,1,3}];

nline=ParametricPlot3D[r[t],{t,-1,1}];

tplane=Plot3D[7/6+x-2y,{x,2,4},{y,1,3}];

Show[graph,tplane,nline,BoxRatios->Automatic,ViewPoint->{3,3,1},AxesLabel->{x,y,z}]