Point of Inflection of a Cubic Function: The general equation of a quadratic function is

Chapter 8, Problem 37

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Point of Inflection of a Cubic Function: The general equation of a quadratic function is y = ax2 + bx + c where a 0 Recall from algebra that the middle of the graph of a quadratic function (that is, thevertex) is at x = b/(2a). The middle of thegraph of a cubic function is at its point ofinflection. Prove that if f(x) = ax3 + bx2 + cx + d,where a 0, then the point of inflection islocated at x = b/(3a)

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