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Find the directional derivative of the function at the given point in the direction of the vector v. f(X. y. 2) = vaz. (4, 2, 8), v = (-1, -2, 2) Duf(4, 2, 3) = _1 X Need Help? i Submit Answer Find the directional derivative of f(x, y, z) = Xy + yz + zx at P(1, 1, 2) in the direction from P to Q(2, 4, 5). Until. -1. Z) = Need Help? 4. [I1 Points] SCALC714.6.021. ASK YOUR TEACHER PRACTICE ANOTHER Find the maximum rate of change offat the given point and the direction in which it occurs. f(X. y) = 4y\\/}, (4, 7) maximum rate of change direction vector ' Need Help? 5. [-/1 Points] DETAILS SCALC7 14.6.025. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the maximum rate of change of fat the given point and the direction in which it occurs. f( x, y, z) = V x2 + y2 +z2, (3, 6, -2) maximum rate of change direction vector Need Help? Watch It Talk to a Tutor 6. [-/1 Points] DETAILS SCALC7 14.6.029.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find all points at which the direction of fastest change of the function f(x, y) = x2 + y2 - 2x - 6y is i + j. (Enter your answer as an equation.) Need Help? Watch It Master It Talk to a Tutor7. [-/1 Points] (c) What is the SCALC7 1 4.6.033. Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 4x2 5xy + xyz (a) Find the rate of change of the potential at P(5, 6, 7) in the direction of the vector v = I +j k. (b) In which direction does V change most rapidly at P? maximum rate of change at P? Need Help? | MY NOTES ASK YOUR TEACH ER PRACTICE ANOTHER l 3. [-I1 Points] SCALC7 14.6.041 . Find equations of the following. 2(x 7)2 + (y 7)2 + (z 4)2 = 10, (8,9,6) (a) the tangent plane (b) the normal line (x(t), y(t), 2(0) = ( ) Need Help? ASK YOUR TEACHER PRACTICE ANOTHER At what point on the paraboloid y = x2 + z is the tangent plane parallel to the plane 3x + 4y + 3z = 4? (If an answer does not exist, enter DNE.) ( x, y, Z ) = Need Help? Talk to a Tutor [-/1 Points] DETAILS SCALC7 14.6.514.XP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTH Consider the following. f(x, y, z) = xe4yz, P(1, 0, 1), u = W N 2 3 (a) Find the gradient of f. Vf ( x, y, z) = (b) Evaluate the gradient at the point P. Vf( 1, 0, 1) = (c) Find the rate of change of f at P in the direction of the vector u. Duf(1, 0, 1) = Need Help? Watch It Talk to a Tutor