5/10/12 9:47 PMSection 11.6Page 1 of 3http://www.webassign.net/web/Student/Assignment-Responses/view_key?dep=3769836Current Score : 24.25 / 24.25 Due : Monday, February 27 2012 11:05 PM EST1. 2/2 points | Previous AnswersFind the directional derivative of f at the given point in the direction indicated by the angle !.f(x,y) = sin(x + 2y)(4, -2)! = 3!/40.707 0.7072. 2/2 points | Previous AnswersFind the directional derivative of the function at the given point in the direction of the vector v.f(x, y, z) = x/(y + z), (4, 1, 1), v = <1, 2, 3>-1.2 -1.23. 1/1 points | Previous AnswersUse the figure to estimate Du f(2, 2).-3 -34. 2/2 points | Previous AnswersFind the directional derivative of f(x, y, z) = x2 + y2 + z2 at P(2, 1, 3) in the direction of the origin.-7.48 -7.485. 3/3 points | Previous AnswersFind the maximum rate of change of f at the given point and the direction in which it occurs.Section 11.6 (Homework)Ali Al ZaabiMA 242, section 001, Spring 2012Instructor: J. Louis CappsWebAssignThe due date for this assignment is past. Your work can be viewed below, but no changes can be made.5/10/12 9:47 PMSection 11.6Page 2 of 3http://www.webassign.net/web/Student/Assignment-Responses/view_key?dep=3769836f(x, y) = ln(x2 + y2), (1, 2)Maximum rate of change0.894 0.894 Direction (Enter as a vector of magnitude 1.)< 0.447 0.447 , 0.894 0.894 >6. 4/4 points | Previous AnswersFind the maximum rate of change and the gradient of f at the given point.f(x, y, z) = x2y3z4, (1, 1, 1)Maximum rate of change5.39 5.39 Gradient< 2 2 , 3 3 , 4 4 >7. 2.25/2.25 points | Previous AnswersNear a buoy, the depth of a lake at the point with coordinates (x, y) is z = 200 + 0.02x2 - 0.001y3,where x, y, and z are measured in meters. A fisherman in a small boat starts at the point (80, 60) andmoves toward the buoy, which is located at (0, 0).(a) Find Du f(80,60).3.92 3.92 (b) Is the water under the boat getting deeper or shallower when hedeparts?8. 5/5 points | Previous AnswersThe temperature at a point (x, y, z) is given by the following where T is measured in °C and x, y, z inmeters.T(x, y, z) = 200e-x2-3y2-9z2(a) Find the rate of change of temperature at the point P(2, -1, 2) in the direction toward thepoint (3, -3, 3). (Do this on paper. Your teacher may ask you to turn in this work.) deepershallower5/10/12 9:47 PMSection 11.6Page 3 of 3http://www.webassign.net/web/Student/Assignment-Responses/view_key?dep=3769836(b) In which direction does the temperature increase fastest at P? (Enter as a vector ofmagnitude 1.)< -0.109 -0.109 , 0.163 0.163 , -0.981 -0.981 > (c) Find the maximum rate of increase at P. °C/m9. 3/3 points | Previous AnswersSuppose that you are climbing a hill whose shape is given by the equation z = 1000 - 0.01x2 - 0.02y2and you are standing at a point with coordinates (60, 100, 764).(a) In which direction should you proceed initially in order to reach the top of the hillfastest? (Enter as a vector of magnitude 1.)< -0.287 -0.287 , -0.958 -0.958 >(b) If you climb in that direction, at what angle above the horizontal (in degrees) will you beclimbing initially?76.5 76.5