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March 30, 2017

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How do I find the minimum or maximum of this y = 2x³ + 3x² - 12x? It makes 2 curves.

  • Pre-Calculus - ,

    y = 2x^3 + 3x^2 - 12x
    y' = 6x^2 + 6x - 12 = 6(x+2)(x-1)

    y'=0 when x=-2 or 1
    Knowing what you do about cubic curves, you can see that

    the local max occurs at x = -2, and
    the local min is at x = 1

    y(-2) = 20
    y(1) = -7

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