Final answer:
The gradient vector of f(x, y) = xy at the point (7, 4) is (4, 7).
Step-by-step explanation:
To find the gradient vector of the function f(x, y) = xy at the point (7, 4), we need to calculate the partial derivatives of f with respect to x and y. The gradient vector is then given by the vector formed by these partial derivatives.
The partial derivative of f with respect to x is y, and the partial derivative of f with respect to y is x. So, the gradient vector at (7, 4) is (4, 7).
Therefore, the gradient vector ᵃf(7, 4) is (4, 7).