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?
Why On a half-wave dipole the standing wave puts maximum current at the center and maximum voltage at the ends. Since impedance is voltage divided by current, the feed point impedance rises steadily as you move away from the center, going from roughly 70 ohms at the middle to several thousand ohms near the tips. That is exactly why an off-center-fed dipole uses a 4:1 or 6:1 balun, and why an end-fed half wave needs a very high impedance matching transformer.
Watch out The idea that it decreases has the current and voltage distribution backwards; there is also no peak partway out, the increase is monotonic all the way to the ends.
Center = high current, low Z (~70 ohms). Ends = high voltage, high Z. Move out, Z goes up.