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)

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f(x, y) = 4y √x, (4, 1)

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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.

The gradient vector of f is

Then, the maximum rate of change is

in the direction of (5,8).