31. H _ F is the Hessian matrix of F ( matrix of the second derivatives ). 32. If they exist, the Collie points of a function are the roots of the second derivative . 33. The market, the second derivatives exchange in Latin America after Brazil, already offers four futures contracts. 34. Evaluation of the related second derivatives allows the prediction of vibrational frequencies if harmonic motion is estimated. 35. :Yes, that is indeed the second derivative . 36. The second symmetric derivative may exist however even when the ( ordinary ) second derivative does not. 37. The different cases may be distinguished by considering the eigenvalues of the Hessian matrix of second derivatives . 38. As the flow is turbulent, its mean profile is logarithmic, and its second derivative is thus negative. 39. Here, \ ddot ( 0 ) is the second derivative of the autocorrelation function evaluated at zero. 40. Calculus allows for a more detailed comparison between the two curves via The First and Second Derivatives .
