The temperature T of a point with coordinates (r, y) lying in a region of the (r, y)-plane is given by the function T(x, y) = 3r' - 2cy + 2x - 3y' + 4y. (a) Determine grad T and evaluate it at the point (1, -1). (b) What is the value of the derivative of T at the point (1, -1) in the direction of the vector d = i - j? (c) Find the maximum rate of change in temperature at the point (1, -1). What is its direction? (d) Show that the temperature is ( at the point (1, -1). At this point. determine the equation of the tangent to the T =0 contour of temperature, in the form y = me + c, where m and c are constants that you should determine