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Math Help - To find steeper tangents....please help!

  1. #1
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    To find steeper tangents....please help!

    Find all values x such that the tangent line to the graph of f(x)=4x^2 + 11x + 2 is steeper than the tangent line to g(x)=x^3

    I think i get stuck while solving quadratic inequalities...

    nybody know how to do this??? please help
    Thanks!
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  2. #2
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    8x + 11 > 3x^2

    0 > 3x^2 - 8x - 11

    0 > (3x - 11)(x + 1)

    two critical values ... x = \frac{11}{3} and x = -1

    the quadratic is negative between the two roots ...

    -1 < x < \frac{11}{3}
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