Graph y = x³/3 - x²/2

Imagine a small circle sitting inside the local minimum. Gravity pulls in the negative y direction so it is quite stable there.

Now increase the size of the circle. At some point it will become too large to fit in this hollow and will be forced to roll away down into the third quadrant.

At what radius does this happen?

When the radius is approximately equal to 2.528162 the circle will become too large to fit in the hollow and will be forced to roll away into the 3rd quadrant.

Posted by K Sengupta on 2022-07-12 22:19:29