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

1. [-11 Points] DETAILS SCALCETQ 14.6.004.EP. Consider the following. x, y} = W3 - x2 Find the partial derivatives. x. 1!} = aux. r} = Find the directional derivative of fat the point {1, 4} in the direction indicated by the angle 9 = E. 3 ouf( 1, 4) = Need Help? 2. [-11 Points] DETAILS SCALCETQ 14.6.005. Find the directional derivative of fat the given point in the direction indicated by the angle 6. x, y} = eceetxy), (a. 1), e = E ouo, 1) = Need Help? 3. [41 Points] DETAILS I SCALCETQ 14.6.0113. Consider the following. 1 fix, y} = x262\". ms. 0). u = Em 3i) (3} Find the gradient of f. \"\"06 y} = {b} Evaluate the gradient at the point P. ms, 0) = (c) Find the rate of change of fat P in the direction of the vector u. euros, o) = Need Help? 4. [-/1 Points] DETAILS SCALCET9 14.6.011. Consider the following. F( x, y, z) = x yz - xyz , P(4, - 1, 1), U= 0 5 ' (a) Find the gradient of f. VA( x, y, Z) = (b) Evaluate the gradient at the point P. VA(4, - 1, 1) = (c) Find the rate of change of fat P in the direction of the vector u. D F(4, - 1, 1) = Need Help? Read It Watch It5. [-11 Points] DETAILS SCALCETQ 14.6.013.EP. Consider the following. x, y} = 7ex sin[y) Find Vx, y). \"TX: y} = Determine Vx, y) at the point (D, E). 3 Vol: 3 Determine a unit vector in the direction of the vector v = (10, 24). Find the directional derivative of the function at the given point in the direction of the vector v. x,y}= 7exsin[y), (0,?) v: (10, 24) Need Help? W 6. [-/1 Points] DETAILS SCALCET9 14.6.017. Find the directional derivative of the function at the given point in the direction of the vector v. f( x, y, z ) = x2y + yzz, (1, 2, 3), v = (2, -1, 2) Duf( 1, 2, 3) = Need Help? Read It 7. [-/1 Points] DETAILS SCALCET9 14.6.022.EP. Consider the following. A( x , V ) = -2 Find VA(x, y). VA( x , y ) = Determine VA(x, y) at the point P = (3, -1). VA(3 , - 1 ) = Determine a unit vector in the direction of PQ where P = (3, -1) and Q = (-6, 11). 1 = Find the directional derivative of the function at the point P in the direction of the point Q. Ax, y ) = 2, P(3, -1), Q(-6, 11) Need Help? Read It8. [-/1 Points] DETAILS SCALCET9 14.6.027. Find the maximum rate of change of fat the given point and the direction in which it occurs. f( x, y ) = 8xyz, (5, -7) maximum rate of change direction vector Need Help? Read It 9. [-/1 Points] DETAILS SCALCET9 14.6.035.MI. Find all points at which the direction of fastest change of the function f(x, y) = x. calculate Duzz, l). ouzz, 1) = Need Help? 12. [-/1 Points] DETAILS SCALCET9 14.6.047.EP. Consider the following function. F(x, y, z) = 2(x - 3)2 + (y - 2)2 + (2 - 5)2 = 10 Find the partial derivatives. F ( x, y, Z ) = Fy ( x, y, z ) = F z (X, V, Z ) = Determine the partial derivatives at the point (4, 4, 7). Fx ( 4 , 4, 7 ) = F ( 4 , 4, 7 ) = F 2 ( 4, 4, 7 ) = Now, consider the following. 2(x - 3)2 + (y - 2)2 + (2 - 5)2 = 10, (4, 4, 7) (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 It13. [-/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 2 X 6 8 X O 4 10 6 12 2 8 14 10 12 14 2 4 6 8 10 X 12 14 2 4 6 8 10 12 14 Need Help? Read It Watch It14. [-/1 Points] DETAILS SCALCET9 14.6.066. At what points does the normal line through the point (1, 2, 1) on the ellipsoid 4x2 + yz + 42 = 12 intersect the sphere x2 + y2 + z2 = 363? smaller x-value ( x, y, Z ) = larger x-value ( x, y, Z ) = Need Help? Read It