Geodesic
Best Error Bounds for the~Derivative of a~Quartic Interpolation Spline
Matematičeskie trudy, Tome 1 (1998) no. 2, pp. 68-78.

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For a quartic $C^2$-spline, G. Howell and A. Varma established the best estimate for an error of interpolation of a smooth function. The article provides an answer to their question on estimating the derivative. We obtain an estimate for the error of approximation to the derivative with a sharp constant. 
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     author = {Yu. S. Volkov},
     title = {Best {Error} {Bounds} for {the~Derivative} of {a~Quartic} {Interpolation} {Spline}},
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Yu. S. Volkov. Best Error Bounds for the~Derivative of a~Quartic Interpolation Spline. Matematičeskie trudy, Tome 1 (1998) no. 2, pp. 68-78. http://geodesic.mathdoc.fr/item/MT_1998_1_2_a2/