Is My Second Derivative Calculation Correct for Finding Inflection Points?

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Discussion Overview

The discussion centers around the calculation of the second derivative for the purpose of finding inflection points of the function (c/((1+ae^(-bx)))). Participants are evaluating the correctness of the second derivative and exploring alternative methods for identifying inflection points.

Discussion Character

  • Homework-related, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses uncertainty about their second derivative calculation, suggesting it may be incorrect.
  • Another participant agrees that the calculation seems plausible but questions the power of the denominator, suggesting it should be a third power instead of a seventh.
  • Some participants propose that inflection points can be identified using the first derivative by setting it to zero and testing points around critical points, indicating that inflection points do not necessarily have to be critical points.

Areas of Agreement / Disagreement

There is no consensus on the correctness of the second derivative calculation, and multiple approaches to finding inflection points are discussed, indicating disagreement on the method.

Contextual Notes

Participants have not resolved the specific mathematical steps involved in the second derivative calculation, and there are differing opinions on the necessity of using the first derivative for finding inflection points.

greko
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I am not sure if this counts as homework but its a complex problem to me. I must find the inflection point of the equation (c/((1+ae^(-bx)))). Therefore I must take the 2nd derivative. Which I got as (abc)(e^(-bx))(abe^(-bx)-b)/((1+ae^(-bx))^7)). And this sounds wrong to me? Can someone tell me if I am on the right track?
 
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I think you're on the right track. The 7th power in the denominator should just be a 3rd power, though - was this a typo, or did you make a mistake? Now what does this equal at the inflection point?
 
You actually should be able to find the inflection point using only the first derivative. Set the derivative equal to zero and then test points on both sides of each zero. If you get matching signs on both sides of a critical point then you have an inflection.
 
Mu naught said:
You actually should be able to find the inflection point using only the first derivative. Set the derivative equal to zero and then test points on both sides of each zero. If you get matching signs on both sides of a critical point then you have an inflection.

Inflection points don't have to be critical points
 

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