New Tab X Content X "A M273 14.6 Derivatives - MAT X - C 20 webassign.net/web/Student/Assignment-Responses/last?dep=33663080 DIO M Relaunch to update : M Gmail YouTube il Courses lil Content * Washington, D.C. t... 0 Review Trip Detail... All Bookmarks Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer. Assignment Scoring Your best submission for each question part is used for your score. 1. [-/3 Points] DETAILS SCALCET9 14.6.011. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following. f(x, y, z) = x2yz - xyz3, P(2, -1, 1). = o, . -3) (a) Find the gradient of f. VA( x, y, z) = (b) Evaluate the gradient at the point P. VA(2, -1, 1) = (c) Find the rate of change of fat P in the direction of the vector u. Duf(2, -1, 1) = Need Help? Read it Watch It Submit Answer 2. [-/2 Points] DETAILS SCALCET9 14.6.001. MY NOTES ASK YOUR TEACHER Level curves for barometric pressure (in millibars) are shown for 6:00 a.m. on a day in November. A deep low with pressure 972 mb is moving over northeast Iowa. The distance along the red line from K (Kearney, Nebraska) to S (Sioux City, Iowa) is 300 km. What are the units of the directional derivative? O km/mb O mb/km O mb/km2 km O mb Estimate the value of the directional derivative of the pressure function at Kearney in the direction of Sioux City. (Round your answer to two decimal places.) Need Help? Read It Submit Answer 3. [-/1 Points] DETAILS SCALCET9 14.6.013 . MY NOTES ASK YOUR TEACHER PRACTICE ANOTHERNew Tab X Content X "A M273 14.6 Derivatives - MAT X - G 20 webassign.net/web/Student/Assignment-Responses/last?dep=33663080 M Relaunch to update : M Gmail YouTube il Courses all Content Washington, D.C. t... 0 Review Trip Detail... All Bookmarks 3. [-/1 Points] DETAILS SCALCET9 14.6.013. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the directional derivative of the function at the given point in the direction of the vector v. ((x , y ) = 7ex sin(y). (0 , 7 ). v = (- 3, 4 ) Need Help? Read it Watch It Submit Answer 4. [-/1 Points] DETAILS SCALCET9 14.6.019. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the directional derivative of the function at the given point in the direction of the vector v. h(r, s, t) = In(3r + 6s + 9t), (1, 1, 1), v = 6i + 18j + 9k Duh( 1, 1, 1) = Need Help? Read It Watch It Submit Answer 5. [-/2 Points] DETAILS SCALCET9 14.XP.6.018. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the maximum rate of change of f at the given point and the direction in which it occurs. 1( x, y) = ByVx, (16, 3 ) maximum rate of change direction vector Need Help? Read it Watch It Submit Answer 6. [-/3 Points] DETAILS SCALCET9 14.6.039. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Suppose that over a certain region of space the electrical potential V is given by the following equation. V ( x, y, z) = 2x2 - 5xy + xyz (a) Find the rate of change of the potential at P(6, 6, 7) in the direction of the vector v = i + j - k. (b) In which direction does V change most rapidly at P? (c) What is the maximum rate of change at P? Need Help? Read it Watch It Submit Answer DETAILS PRACTICNew Tab X Content X "A M273 14.6 Derivatives - MAT X - C 2 webassign.net/web/Student/Assignment-Responses/last?dep=33663080 M Relaunch to update : M Gmail YouTube Courses all Content Washington, D.C. t... 0 Review Trip Detail... All Bookmarks . [-/2 Points] DETAILS SCALCET9 14.6.047. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following 2(x - 5)2 + (y - 2)2 + (2-9)2 = 10, (6, 4, 11) (a) Find an equation of the tangent plane to the given surface at the specified point. (b) Find an equation of the normal line to the given surface at the specified point. ( x (t), y(t), z(t) = Need Help? Read it Watch It Submit Answer 8. [-/3 Points] DETAILS SCALCET9 14.6.055. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER If f(x, y) = xy, find the gradient vector Vf(4, 3). VA( 4 , 3 ) = Use the gradient vector to find the tangent line to the level curve f(x, y) = 12 at the point (4, 3). Sketch the level curve, the tangent line, and the gradient vector. 12 10 2 6 8 810 12 O-2 2 10 12 2 4 10 14 Need Help? Read It Watch It Submit Answer 9. [-/1 Points] DETAILS SCALCET9 14.XP.6.002. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the directional derivative of f at the given point in the direction indicated by the angle 8. (x, y) = 2ye-*, (0, 3), 8 = 27 DJ"(0, 3) = Need Help? Read it Watch It Submit