Consider the following. f(x, y) = x/y, p(9, 1), u = 3 5 i + 4 5 j (a) find the gradient of f. ∇f(x, y) = (b) evaluate the gradient at the point p. ∇f(9, 1) = (c) find the rate of change of f at p in the direction of the vector u. duf(9, 1) =

The rate of change of f at P in the direction of the vector u is 7.8

Given the function at the point P(9, 1) where the vector

a) To get the gradient of "f"

b) Substituting x = 9 and y = 1 into the result in (a), we will have:

c) We need to get the derivative of ∇f(9, 1) in the direction of the vector

The formula for the derivative in the direction is expressed as;

Get the modulus of the vector |u|

Substitute the given parameters into the derivative formula:

Hence the rate of change of f at P in the direction of the vector u is 7.8

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a. The gradient is

b. At the point (9, 1), the gradient has value

c. The derivative of at (9, 1) in the direction of is

We have

so