1. [-/3 Points] DETAILS SCALCET8 14.6.009. MY NOTES PRACTICE ANOTHER Consider the following. f ( x, y, z) = x2yz - xyz, P(4, - 1, 1), u= (0, UT / W (a) Find the gradient of f. Vf ( x, y, z) = (b) Evaluate the gradient at the point P. Vf( 4, - 1, 1) = (c) Find the rate of change of f at P in the direction of the vector u. Duf(4, -1, 1) =Level curves for barometric pressure (in millibars) are shown for 6:00 AM 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. 1012 1016 1008 1020 1024 1012 -1004 -1000 996 .992 988 984 980 S 976 972 1008 Estimate the value of the directional derivative of the pressure function at Kearney in the direction of Sioux City. What are the units of the directional derivative?3. [-/1 Points] DETAILS SCALCET8 14.6.011. MY NOTES PRACTICE ANOTHER Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y) = 3ex sin(y), (0, 1/3), v = (-10, 24) Dvf(0, 1/ 3) = Need Help? Read It Watch It4. [/1 Points] DETAILS SCALCET8 14.6.017. MY NOTES PRACTICE ANOTHER Find the directional derivative of the function at the given point in the direction of the vector v. h(r, s, t) = |n(3r+ 65 + 9t), (1, 1, 1), v = 14i + 42j + 21k Dvh(1, 1,1) = 5. [I2 Points] DETAILS SCALCETS 14.6.021. MY NOTES PRACTICE ANOTHER Find the maximum rate of change of fat the given point and the direction in which it occurs. f(X. y) = 8N}, (16, 5) maximum rate of change direction vector 6. [I3 Points] DETAILS SCALCETS 14.6.033. MY NOTES 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 4xy + xyz (a) Find the rate of change of the potential at P(4, 4, 6) 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? 7. [l2 Points] DETAILS SCALCET8 14.6.041. MY NOTES PRACTICE ANOTHER Find equations of the following. 2(x 9)2 + (y 2)2 + (z 3)2 = 10, (10, 4, 5) (a) the tangent plane (b) the normal line W), m), 2m) = ( ) 8. [1/3 Points] DETAILS PREVIOUS ANSWERS SCALCET8 14.6.049. MY NOTES PRACTICE ANOTHER If f(X, y) = xy, find the gradient vector Vf(6, 5) and use it to find the tangent line to the level curve f(X, y) = 30 at the point (6, 5). gradient vector tangent line equation