First and Second Derivatives dealing with prices of stock

[Jacobpm64]

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."
(b) "The price of the stock is close to bottoming out."


My answers:
(a) P'(t) > 0, P''(t) > 0

(b) Does anyone know what "bottoming out" means? I never dealt with the stock market. If i knew what that term meant, I'm sure I could figure it out.

 

[cepheid]

Your answer for part (a) looks right to me.

As for part (b), keep in mind that "bottoming out" is not a technical "stock market" term. In fact, it's an everyday speech term. For something to bottom out means for it to become as low as it possibly can go (to "hit the bottom", so to speak). It does not go any lower than this value for any time, t. Let me ask you a question: what is the proper mathematical term describing such a situation?

 

[Jacobpm64]

oh, so it's close to approaching a minimum?

So, P'(t) < 0, P''(t) > 0 eh?