Find the directional derivative of x, y, z) = xy223 at P(3, 1, 1) in the direction of Q(O, 5, 7). sum, 1, 1) = 3.84 X The temperature Tin a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1, 2, 2) is 130. (a) Find the rate of change of Tat (1, 2, 2) in the direction toward the point (3, 1, 4). 520 27 Suppose that over a certain region of space the electrical potential V is given by the following equation. V(X, y, z) = 5x2 2xy + xyz (a) Find the rate of change of the potential at P(6, 4, 4) in the direction of the vector v = i + j k. 56 / (b) In which direction does Vchange most rapidly at P? 48i+ 12j +241; X (c) What is the maximum rate of change at P? 4\/ 443 X Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to use a calculator or computer to graph the function with a domain and Viewpoint that reveals all the important aspects of the function. (Enter your answers as commaseparated lists. If an answer does not exist, enter DNE.) f(X, y) = x3 + y3 3X2 6y2 9X local maximum value(s) 5 / local minimum value(5) 59 / saddle point(s) (x, y) = (3.0) Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to use a calculator or computer to graph the function with a domain and Viewpoint that reveals all the important aspects of the function. (Enter your answers as commaseparated lists. If an answer does not exist, enter DNE.) x: V) = y2 6y cos(x), 4 g x g 4 local maximum value(s) local minimum value(s) *9 saddle point(s) (X, y) = ((17 + %)T[,U)