Some questions on the gradient. (1) Suppose f (r, y) is the temperature (in "C) of a flat sheet of metal at position (r, y) (in cm). Suppose Vf (7, 2 ) = (-2, 4) Suppose an ant walks on the pan. It's position (in cm) at time t (in s) is given by F(t). We have F(6) = (7,2) and F' (6) = (-3, 4) By "the temperature of the ant," we mean the temperature at the position of the ant. (a) What are the units of Vf? (b) How would you interpret ' (6) = (-3, 4) within this problem? Answer using a sentence about the ant. Include units in your answer. (c) What is the instantaneous rate of change of the temperature of the ant per second of time, at time t = 6 s? Include units in your answer. (d) What is the instantaneous rate of change of the temperature of the ant per centimeter the ant travels, at time t = 6 s? Include units in your answer. (e) Standing at the point (7, 2), in which direction should the the ant walk so it's instantaneous rate of change of temperature will be as rapid as possible? Give your answer as a unit vector. (f) If the ant at (7, 2) walks in the direction given by (e), what will be the instantaneous rate at which the ant warms up per cm travelled at that moment? Include units in your answer. (g) If the ant at (7, 2) walks in the direction given by (e) at a rate of 3 cm/s, what will be the instantaneous rate at which the ant warms up per second at that moment? Include units in your