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advanced functions

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Solve the inequality 12x^3 + 8x^2 <= 3x + 2. Justify your answer.

  • advanced functions -

    12x^3 + 8x^2 ≤ 3x + 2
    12x3 + 8x^2 - 3x - 2 ≤ 0

    after some trial and errors where I tried
    x = ±1, ±2, etc, I found
    x = ±1/2 and x = -2/3 give me zero

    12x3 + 8x^2 - 3x - 2 ≤ 0
    (2x-1)(2x+1)(3x+2) ≤ 0

    knowing the behaviour of
    y = 12x3 + 8x^2 - 3x - 2
    and having x-intercepts of -2/3, -1/2 and +1/2

    the solution would be
    x ≤ -2/3 OR -1/2 ≤ x ≤ 1/2

    confirmation:
    http://www.wolframalpha.com/input/?i=plot+12x3+%2B+8x%5E2+-+3x+-+2+≤+0

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