solve the answers handwritten but please type all the final answers together in the different section after solving. Thanks.

8. {-11 Points] DETAILS SCALCET9 145.027. Find the maximum rate of change of fat the given point and the direction in which it occurs. x, y) = 8W2. (5. 7) Need Help? maximum rate of change direction vector 9. [I1 Points] DETAILS SCALCET9 14.6.035.Ml. Find all point5 at which the direction of fastest change of the function f(x, y) = x2 + y2 4x 6y isi + j. (Enter your answer as an equation.) Z Need Help? 10. [41 Points] DETAILS SCALCE'I'9 14.6.038. The temperature at a point (x, y, 2) is given by 2 2 2 T(x, y, z) = 4009\" ' 5" _ 9'7 where T is measured in \"C and x. 1!. Z in meters' (a) Find the rate of change of temperature (in C!m} at the point H2, 1, 5} In the direction toward le point (3, 5, 6). dc/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P. Need Help? 11. [-H Points] DETAILS SCALCETQ 14.6.0135. The second directional derivative of x. 1!} is Duzx, y} = D\" [Outta 101' Ifx. y) = x3 + szy + Y3 and u = (i E). calculate DHJKZ, 1). 13' 13 2 _ Du 2' 1) |:| Need Help? 12. [-11 Points] DETAILS SCALCET9 14.5.041EP. Consider the following function. F(x. y. z) = 2(x7 3)2 + (y7 2)2 + (27 5)2 = 10 Find the partial derivatives. nix, y, z) = FAX. r. z} = inm in 2) Determine the partial derivatives at the point (4, 4, 7). mm = |:I w. 4. n : |:| w. 4. n = |:| Now, consider the following. 2(x 3)2 + (y 2)2 + (z 5)2 = 10. (4. 4. 7) (a) Find an equation of the tangent plane to the given surface at the specied point. (b) Find an equation of the normal line to the given surface at the specied point. W). M: (E ) Need Help? _' 13. [-/1 Points] DETAILS SCALCET9 14.6.055. If f(x, y) = xy, find the gradient vector VF(4, 3). MY NOTES ASK YOUR TEACHER PRAC 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. 14/ 12 12 12- 14 10 10 10 12 8 8 8 10 6 6 8 4 4 4 2 2 4 2 6 8 X 2 2 4 X 10 12 6 8 14 10 12 14 2 4 6 8 10 14 @0-2 2 4 8 10 12 14 Need Help? Read It Watch It14. [-11 Points] DETAILS SCALCET914.6.066. At what point: does the normal line through the point (1, 2, 1) an the ellipsoid 4x2 + y2 + 422 = 12 intersect the sphere x2 + y2 + z2 = 363? smaller xvalue (x, y, z) = (I: ) larger xvalue (x, y, z) = ( |:| ) Need Help