The correct answer is A) it decreases with latitude, being maximum at the geographic equator. The directive force of a gyrocompass is the force that aligns the gyro rotor with true north. This directive force is generated by the Earth's rotation and is strongest at the geographic equator, where the rotation of the Earth is most pronounced. As you move away from the equator towards the poles, the directive force decreases, as the rotation of the Earth becomes less pronounced. The other options are incorrect because: B) the directive force does not remain the same at all latitudes, C) the directive force is not greatest near the magnetic equator, and D) the directive force increases towards the poles, not the geographic equator.