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

the answer is 175.4379

step-by-step explanation:

a

step-by-step explanation:

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