Homework SourseIf fx y z 3x2 2y2 z2 find the dot product of grad f with
If f(x, y, z) = 3x2 + 2y2 + z2, find the dot product of grad f with itself.
A)4(x2 + y2 + z2)
B)4(x2 + 4y2 + 9z2)
C)4(4x2 + y2 + 9z2)
D)4(9x2 + 4y2 + z2)
E)4(16x2 + 4y2 + 9z2)
F)4(9x2 + 16y2 + 9z2)
G)4(16x2 + 9y2 + 16z2)
H)There is no such thing.
I)There is such a thing, but it\'s none of these.
Solution
grad(f)=(df/dx,df/dy,df/dz)=(6x,4y,2z) grad(f)*grad(f)=(6x,4y,2z)*(6x,4y,2z)=(36x^2+16y^2+4z^2)= =4(9x^2+4y^2+z^2) It is D
