Consider the function h(x,y,z) = ram\"'3' + sin(2:rz). (a) (i) Calculate the gradient of h. (4 marks} (ii) Hence, determine the directional derivative of h at the point (2, 5,1) in the direction 3i - I + k. (4 marks} (b) Now, consider the level surface 310nm) = 1- (i) 1'v'erify that (2, 5, 1) is a point on the level surface. (I mark} (ii) Comment about the relation between the gradient of h at the point (2, 5, 1) and the level surface. (2 marks} (iii) Hence, or otherwise, determine the maximum rate of change of h at the point (2.5.1)- (4 marks}