How does the feed point impedance of a 1/2 wave dipole change as the feed point is moved from the center toward the ends?

In a resonant half-wave dipole, the RF current is at its maximum at the center and drops to zero at the ends. Conversely, the RF voltage is at its minimum at the center and reaches its maximum at the ends. According to Ohm's Law (Impedance = Voltage / Current), dividing a low voltage by a high current yields a low impedance (about 73 ohms at the center). As you move the feed point toward the ends, the voltage increases and the current decreases, meaning the impedance steadily increases. At the very ends, the impedance is in the thousands of ohms. Distractors suggesting it decreases or peaks at an arbitrary point fail to account for the smooth sinusoidal distribution of voltage and current along the half-wave wire.