Student is asked to investigate how the function , given by f(x, y, z)=z-(x + y xy) behaves at the point P(1, 2,3). 3.1 Obtain gradf, and hence obtain the value of this vector at the point P. Round components to four decimal places, where necessary. 3.2 Verify whether or not gradf in 3.1 is solenoidal. 3.3 Obtain the (x, y, z) coordinates of all critical points of z = g(x, y) = x + y - xy. 4 3.4 Determine the type of critical points of g(x, y) = x + y xy using second derivative test.