7. Let r(t) =(t-1)'i -4tj-t'k, t:0 ->10 be the position function of a bug at time t, and f(x, y, z) = xy' +3z be the temperature function at (x, y, z) . Find the rate of change of temperature observed by the bug at the point (1, -8, -8) . 8. Suppose that the temperature at (x, y) is given by the function f(x, y) = x y'. A bug is sitting at the point (1, -2) , feeling cold and disoriented. (a) If the bug decides to move in the southwest direction, will it instantly feel warmer or colder? What is the rate of change of temperature observed by it? (b) In which direction should be bug move in order to warm up most rapidly? What is the fastest rate at which it can warm up