Second Derivative of 3x^5 - 5x^3: Inflection Points

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Discussion Overview

The discussion revolves around the second derivative of the function f(x) = 3x^5 - 5x^3, specifically focusing on the identification of inflection points. Participants are examining the correctness of their calculations and comparing them to answers provided in a placement document.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant computed the second derivative as f''(x) = 60x^3 - 30x and identified inflection points at -1/sqrt(2), 0, and 1/sqrt(2).
  • Another participant confirmed the first computation and noted that the placement document provides a different second derivative, 4x(4x^2 - 3), leading to inflection points at -sqrt(3)/2, 0, and sqrt(3)/2.
  • There is a suggestion that the placement document contains multiple mistakes, with specific reference to the derivative of ln(..) in another question.
  • A participant pointed out an error in the derivative of ln(2t^3 - 1), indicating a discrepancy in the placement document's answer.

Areas of Agreement / Disagreement

Participants generally agree that there are mistakes in the placement document, but there is no consensus on the correct identification of the inflection points based on the differing second derivative calculations.

Contextual Notes

Participants have noted potential errors in the placement document, but specific assumptions or definitions that may affect the calculations have not been fully explored.

Rasalhague
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http://www.math.northwestern.edu/courses/placement/220_Self_Placement.pdf

Question 7 here involves a function with the rule f(x) = 3x5-5x3. I computed the 2nd derivative as f''(x) = 60x3-30x (Mathematica agrees.), giving inflection points for f at -1/sqrt(2), 0, 1/sqrt(2). But the answer given in the PDF is 4x(4x2 - 3), whence they conclude the inflection points are -sqrt(3)/2, 0, sqrt(3)/2. Is this a mistake, or have I overlooked something?
 
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You are right, and that is btw not the only mistake in that pdf.
 
Thanks for confirming that, Norwegian. Could you tell me any others, or do you know if there's a list of errata anywhere online?
 
1d, derivative of ln(..) seems wrong, probably more mistakes too
 
Oh yes, wow, so it is! The derivative of ln(2t3-1) is 6t2/(2t3-1), not 6t2/(ln(2t3-1)). When I was checking my answers for those simple ones at the beginning and saw they had something slightly different for 1d, I just assumed it was a typo on my part and didn't look that closely.
 

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