A brand new stock is also called an initial public offering. This model predicts the percent overvaluation of a stock as R(t)=9t((t-3)^3/2.718) where is the overvaluation in percent and t is the time in months after the initial issue.
Use the information provided by the first derivative, second derivative to find the inflection point, the local maximum/minimum, and any false signals.
I figured out that the first derivative is R't=9/2.718(t-4)^2 (4t-4) and the second one is R"(t)=9/2.718(t-4)(12t-24). Would the inflection point be at (4,0) and would the local min be at (1,-89.4)? there also wouldnt be a local max right? Also, what are false signals?
Since R"=0 at t=2 and t=4, I see two inflection points.
R'=0 at t=1 and t=4. Since R' and R" are both zero at t=4 (because of the multiple root there), there is no max/min at t=4. At R"(1)>0, so that's a local minimum.
Not sure about the false signals. I'm sure you can google the terms used in investing, and get many explanations. Just off hand, I'd say that the inflection point at t=4 would be such a signal. The stock price has been rising, but slowing down, and appears ready to fall, but selling would be a bad idea, since it's poised to take off again.
To find the inflection point, local maximum/minimum, and any false signals, we can analyze the first and second derivatives of the function.
First, let's determine the inflection point. An inflection point occurs when the second derivative changes sign. In this case, the second derivative is R"(t) = 9/2.718(t-4)(12t-24).
Setting R"(t) = 0, we can solve for t:
9/2.718(t-4)(12t-24) = 0
By setting each factor to zero, we find two possible values for t: t = 4 and t = 2.
Since we are only interested in the inflection point, we need to determine whether R"(t) changes sign at these points. To do that, we can test the sign of R"(t) by choosing values near t = 4 and t = 2.
For t = 3, R"(t) = 9/2.718(3-4)(12*3-24) = 9/2.718(-1)(36-24) = -108/2.718 < 0, indicating a change in sign.
Therefore, the inflection point occurs at (4,0) because the second derivative changes sign from negative to positive.
Next, let's find any local maximum/minimum. To do this, we need to determine the critical points, which are the values of t where the first derivative is equal to zero or undefined.
The first derivative is R't = 9/2.718(t-4)^2 (4t-4).
Setting R't = 0, we can solve for t:
9/2.718(t-4)^2 (4t-4) = 0
By setting each factor to zero, we find two possible values for t: t = 0 and t = 1.
To determine whether these are local maximum/minimum, we can test the sign of R't around these points.
For t = 0.5, R't = 9/2.718(0.5-4)^2 (4*0.5-4) = 9/2.718(-3.5)(-3) = -94.5/2.718 < 0, indicating a local minimum.
Therefore, the local minimum occurs at (0.5, -94.5) or (1, -94.5).
Regarding false signals, in the context of stock prediction, false signals refer to situations where a trading indicator or model predicts an incorrect outcome, leading to potential losses or poor investment decisions. In this case, false signals could occur if the model predicts overvaluation or undervaluation of the stock in a way that is not consistent with the actual market trends or investor behavior.
To determine if there are any false signals, we would need to compare the model's predictions with the actual observed market behavior and investor reactions.
In summary:
- The inflection point occurs at (4,0).
- The local minimum occurs at (0.5, -94.5) or (1, -94.5).
- There doesn't appear to be a local maximum based on the provided information.
- False signals refer to situations where the model predicts incorrect outcomes, and further analysis is needed to assess their occurrence.