Let [math] represent the price of a share of stock of a corporation at time [math]. What does each of the following statements tell us about the signs of the first and second derivatives of [math]?

(a) The price of the stock is rising faster and faster.
The first derivative of [math] is
The second derivative of [math] is

(b) The price of the stock is just past where it bottomed out.
The first derivative of [math] is
The second derivative of [math] is