college algebra

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determine the vertical asymptotes of the graph of function.g(x)=x^3 diveded by 5x^3-x^2-22x

  • college algebra -

    b(x) = x^3/(5x^3 - x^2 - 22x)
    = x^2/(5x^2 - x - 22) , after dividing by x , x≠0

    f'(x) = (2x(5x^2 - x - 22) - x^2(10x - 1) )/(5x^2-x-22)^2

    to have a vertical tangent, the slope must be undefined, that is
    the denominator of the above f'(x) must be zero

    5x^2 - x - 22 = 0
    (5x-11)(x+2) = 0

    two vertical asymptotes:
    x = 11/5 and x = -2

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