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Web we have been learning how the first and second derivatives of a function relate information about the graph of that. The following problems illustrate detailed graphing of. Since f '' is the first derivative. Web graphing of functions using first and second derivatives. What is the relationship between the first and second derivatives of a function? Web if the original graph is of a parabola, rather than a circle, then the graph of the derivative is a straight line, since d/dx[ax² + bx + c] =. Web f' is the derivative of f, and f'' is the second derivative of f, which is the first derivative of f'. Web the first derivative test provides an analytical tool for finding local extrema, but the second derivative can also be used to.