5. [-/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- 3xy+ xyz (a) Find the rate of change of the potential at P(6, 2, 5) 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 6. [-/1 Points] DETAILS SCALCET9 14.6.045. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The second directional derivative of f(x, y) is DJ 2f ( x, y ) = Du Duf(x, y). If f(x, y) = x3 + 5x2y + y3 and u= (5 12) 13' 13/ calculate D, f( 2, 3). DJ f ( 2, 3 ) = Need Help? Read It Watch It Submit Answer 7. [-/2 Points] DETAILS SCALCET9 14.6.050. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following. xy + yz + zx = 9, (1, 1, 4) (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 Submit Answer 8. [-/2 Points] DETAILS SCALCET9 14.6.060. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER At what point on the ellipsoid x2 + y2 + 9z2 = 1 is the tangent plane parallel to the plane x + 2y + z = 1? smaller x-value ( x, y, z ) = larger x-value ( x, y , z ) = Need Help? Read It