Calculate the actual values of the partial derivatives at

Question

The function in the previous problem is f (x, y) = x(x - 1) (x - 2) + (y - 1)(x - y).

a) Calculate the actual values of the partial derivatives at (3/2, 1/2) and (1, 1).

b) At (3/2, 1/2), find the unit vectors (a, b) such that the derivative of f along the line x(t) = (3/2) + at, y(t) = (½) + bt is zero.

c) Find the points where f_x = f_y = 0, and calculate the second partial derivatives f_xx and f_yy at these points.