Determine the maximum rate of change of the function f at the point p, and in the direction in which it occurs (written as a unit vector).
f(x,y,z) = sqrt(xyz), p = (3,3,2)
I only need help on the first part of this problem:
This is what I did:
Gradient of f = (1/2)(x * y^2 * z^2, x^2 * y * z^2, x^2 * y^2 * z)
I evaluated the Gradient of f at (3,3,2) and attained (54, 54, 81)
So, the maximum rate of change is the magnitude of the Gradient and that is sqrt(54^2 + 54^2 + 81^2) = 111.32385.
Can anyone spot my mistake here? I got the second part right which is just the Gradient vector divided by the magnitude 111.32385; I don't understand how the above is wrong.
Thanks for any help.
f(x,y,z) = sqrt(xyz), p = (3,3,2)
I only need help on the first part of this problem:
This is what I did:
Gradient of f = (1/2)(x * y^2 * z^2, x^2 * y * z^2, x^2 * y^2 * z)
I evaluated the Gradient of f at (3,3,2) and attained (54, 54, 81)
So, the maximum rate of change is the magnitude of the Gradient and that is sqrt(54^2 + 54^2 + 81^2) = 111.32385.
Can anyone spot my mistake here? I got the second part right which is just the Gradient vector divided by the magnitude 111.32385; I don't understand how the above is wrong.
Thanks for any help.