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The graph of the function y= x3+6x2+7x-2cos x changes concavity at x=

  • concavity -

    Concavity changes sign where the second derivative is zero. That would be where
    6x + 12 + 2 cosx = 0, which can also be written
    3x + 6 + cosx = 0

    This transcendental equation will have to be solved numerically by iteration.
    If x = -2, 3x + 6 + cosx = -0.42
    If x = -1.9, 3x + 6 + cosx = -0.02
    -1.9 is close to the correct answer

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