acceleration

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Sorry, no one that I know of say any such thing, the ball potential energy is at max however and the kinetic energy is zero.

The acceleration after it leaved your hand is constant at roughly 9.9 meters/sec or 32 ft/sec.

footnote assuming a straight in the air launch and disregarding air resistance.

In Newtonian physics--the acceleration (on Earth) is constant--32 ft/s^6, 9.8 m/s^2

What changes when you throw a ball in the air is velocity, the velocity is zero when it reaches the top of the arc--not the acceleration.

Rap

The ball has no vertical component of velocity at the peak of its trajectory. Gravity is always pulling down at a constant rate as raprap said. So the acceleration does not change in time.

In math, especially calculus, the maximum and minimum values are the highest and lowest points on a graph respectively. The graph in the x-y plane of a ball thrown is always a parabola (unless thrown straight up). If you graph the velocity of the ball as it changes in time, you will a straight line (v =v0 + at). So the velocity has no maximum value because it has no peak. It is the vertical height that is at a maximum. And the acceleration is always constant (-9.81 m/s^2 or -32.2 ft/s^2). So if you graphed the acceleration with time you will get a straight line.