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Tue 27 Sep, 2005 12:10 am
P(t) is the price of a share of stock of a corporation at time t.
"the price of the stock is rising faster & faster": what does this tell us about the signs of first and second derivatives of P(t)?
i thought the first derivative should be positive since the "velocity" is increasing.
"the price of the stock is close to bottoming out": what does this tell us about the signs of first and second derivatives of P(t)?
i'm not sure.. but by saying "bottoming out", does the graph kind of looks like a concave up graph and the point is at the minimum value? So the second derivative should be positive? what about the first derivative? Thanks~
If the velocity is positive, the first derivative is positive, regardless of if the velocity is increasing or decreasing. In the first case, the stock price is rising, so the first derivative is positive. In the second case it is negative.
The second derivative is the rate of change of velocity. In the first case, the velocity is positive and increasing. Since the velocity is increasing, the second derivative is positive. In the second case, the velocity is negative, but increasing towards zero, so the second derivative is also positive.
Graphically, you are right. Both curves are concave up, so positive second derivative.
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