Final answer:
The magnitude of force F at the point where x = y = 1 m is calculated by multiplying the partial derivative condition with the product of the coordinates, resulting in a force of 4 N.
Step-by-step explanation:
To determine the magnitude of the force F when d = 1.0 m, we can use the fact that the magnitude of the force at the point x = y = 1 m is given by multiplying the partial derivative condition with the product of the coordinates x and y. Thus, the force F at x = y = 1 m is (4 N/m³) × (1 m) × (1 m) = 4 N. The formula arises from the student's question which states that the conservative force satisfies the condition (dFx/dy) = (dFy/dx) = (4 N/m³) xy. This indicates that the net force in that region can be found by differentiating the force in one axis with respect to the perpendicular axis and is given by the product of the differentiation constant and the coordinates.