Originally Posted by

**ebaines**

Yes, but it might be easier to think of the 2nd derivative as the rate of acceleration. If the second derivative is positive this means the surface area is accelerating with increasing value of radius. If negative, this means the area is decelerating with increasing radius. If zero this means the area is changing at a constant rate.

Not quite. If the 2nd derivative is at a minimum and is negative that means it's rate if deceleration has bottomed out and is starting to decelerate less quickly. If it's at a minimum and positvie that means its acceleration is getting bigger.

It doesn't really. In minima/maxima problems you typically look for the point where the 1st derivative is zero and then if the 2nd derivative is positive you know you have a local minimum and if the 2nd derivatie is negative it's a local maximum.