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Second derivativeby Rasalhague
Tags: derivative 
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#1
Feb2012, 09:43 PM

P: 1,402

http://www.math.northwestern.edu/cou..._Placement.pdf
Question 7 here involves a function with the rule f(x) = 3x^{5}5x^{3}. I computed the 2nd derivative as f''(x) = 60x^{3}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(4x^{2}  3), whence they conclude the inflection points are sqrt(3)/2, 0, sqrt(3)/2. Is this a mistake, or have I overlooked something? 


#2
Feb2112, 01:36 AM

P: 144

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



#3
Feb2112, 09:11 AM

P: 1,402

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



#4
Feb2112, 01:10 PM

P: 144

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



#5
Feb2112, 02:14 PM

P: 1,402

Oh yes, wow, so it is! The derivative of ln(2t^{3}1) is 6t^{2}/(2t^{3}1), not 6t^{2}/(ln(2t^{3}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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