# Second derivative

#### Rasalhague

http://www.math.northwestern.edu/courses/placement/220_Self_Placement.pdf [Broken]

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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#### 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.

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