Find the maximum rate of change off at the given point and the direction in which it occurs. f(x, y) = 4y √x, (4, 1)

Answer:

This is the answer for find the maximum rate of change of f at the given point and the direction in which it occurs?

The maximum rate of change of f at the point (4,1) is:

So let’s find fx and fy:

The direction in which the maximum rate of change occurs at point (4,1) is given with:

Vf(4,1) = (1,8)

Remember that the maximum rate of change of f at a point u is the length of the of gradient vector evaluate in u, and the direction in which it occurs is in direction of the gradient vector evaluate in u.