# [SOLVED] find the maximum rate of change of f at the given point and the direction in which it occurs.

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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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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)

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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).

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