You roll a marble down a playground slide that starts level, then curves downward, and finally curves very gradually upward so that it's level again at the end. Where along its travel does the marble experience its greatest acceleration? its greatest speed?

Greatest acceleration at end of downward curve before the upward curve

Greatest speed at end of upward curve before the final plain level

Explanation:

Notice that the marble will experience highest speed and highest  acceleration at different points.

Now, part by part we can examine.

It is obvious that at initial level or plain, no acceleration occurs but speed is same. Now, when the first curve occur, it is downward, so marble will start to accelerate. It is assumed that it is inclined motion, So acceleration will be

a = gsinФ(1)

Now Ф(1) is the angle this inclined motion is creating with x plane.

Now on the second curve, notice that this curve is slightly upward but not plain, so still, there is increase in speed, but acceleration will reduce because again

a = gsinФ(2)

but Ф(1) greater than Ф(2)

so acceleration at downward curve will be greater than acceleration at upward curve. But speed will be increasing before the final straight level come. Because when straight level starts, it will be only friction against the inertia of marble and both will be acting along x axis but in different directions, so, speed just before this final straight level will be highest.

do you have a formula possibly