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

[Rasalhague]

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?

 

[Norwegian]

You are right, and that is btw not the only mistake in that pdf.

 

[Rasalhague]

Thanks for confirming that, Norwegian. Could you tell me any others, or do you know if there's a list of errata anywhere online?

 

[Norwegian]

1d, derivative of ln(..) seems wrong, probably more mistakes too

 

[Rasalhague]

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.