Supposet that f(x,y)= The temperature of a sheet of metal (in°C)at the position (z,y) (in cm) Suppose that VJ (2,3)=(5,12) Suppose that an ant is crawling on the pan. At t=5s, the position of the ant is (2,3) cm, and the velocity of the ant is (3, 4) cm/s. For each of the following questions, show how you get your answer.
(a) At t= 5s, at what (instantaneous) rate is the ant warming up (assume the ant always has the same temperature as the metal it is standing on). Your a answer chould be in
(b) At t = 58, at what (instantaneous) rate is the ant warming up per cm it travels? Your answer should be in C
(c) If the position of the ant is (2,3) cm, in which direction should the ant move to maximize the instantaneous rate it warms up? Give your answer as a unit vector.
(d) If the posiiton of the ant is (2,3) cm and it is travelling in the direction given by (c), at what instantaneous rate is it warming up per cm it travles? Give your answer in cm C
(e) If the posiiton of the ant is (2,3) cm and it is travelling in the direction given by (c) with a speed of 4 at what instantaneous rate is it warming up with respect to time? Give your answer in