Let $P(t)$ represent the price of a share of stock of a corporation at time $t$. What does each of the following statements tell us about the signs of the first and second derivatives of $P(t)$?

(a) The price of the stock is rising faster and faster.
The first derivative of $P(t)$ is ? positive zero negative
The second derivative of $P(t)$ is ? positive zero negative

(b) The price of the stock is just past where it bottomed out.
The first derivative of $P(t)$ is ? positive zero negative
The second derivative of $P(t)$ is ? positive zero negative