>>12955773Think in terms of energy imparted to the ball from gravity. Unless the curve up is higher than the curve down, the energy is greater the steeper the fall because the acceleration is square.
Since acceleration is a square, the amount of energy gained by falling is always greater than the amount of energy lost by the extra distance it has to go.
So regardless of how much longer you can make the path between the two points by curving the line, as long as the curve down is greater than the curve up minus the linear path, and as the displacement in space is the same same, the one with the greater energy will get there first.
