Calculus, Functions

please provide a detailed answer

2. Consider the function f(I, y, 2) = vy'z - Dy - 6+2sin(2y -32), and the point P = (1, 3, 2) . (a) 1 mark. Calculate f (1, 3, 2). (b) 7 marks. Calculate f, (1, 3, 2). (c) 7 marks. Calculate fy (1, 3, 2). (d) 7 marks. Calculate f= (1, 3, 2). (e) 2 marks. Find unit vectors in the directions in which f increases and decreases most rapidly at the point P. (f) 1 mark. Find the rate of change of f at the point P in these directions. Show the details of your work