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Help with inverse of derivative function

  1. Jan 17, 2015 #1
    • Member warned about not using the homework template
    f(x) =
    sqrt2a.gif 3x^3 + 3x^2+ 2x + 1
    ,a = 3

    formal is img5.gif

    Homework is due tonight and this is the only problem i cant solve

    Your suppose to
    3=
    sqrt2a.gif 3x^3 + 3x^2 + 2x + 1
    , solve for xThe find the derivative of y=
    sqrt2a.gif 3x^3 + 3x^2 + 2x + 1
    , then plug x into that and put it under 1.
     
  2. jcsd
  3. Jan 17, 2015 #2

    Mark44

    Staff: Mentor

    What does a represent? I infer from your work below that you are taking it to mean the point (x0, a) on the graph of f.
    Assuming that your interpretation is the correct one, start with this equation:
    ##3 = \sqrt{3x^3 + 3x^2 + 2x + 1}##, and then square both sides. The resulting equation is not the easiest to solve, but it does have one real solution.
     
    Last edited: Jan 17, 2015
  4. Jan 17, 2015 #3
    Yes that is it but sadly i cannot solve it
     
  5. Jan 17, 2015 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You want to solve ##p(x) = 0##, where ##p(x) = 3 x^3 + 3 x^2 + 2x - 8##.
    (i)One thing to try is the "rational root theorem"; see, eg.,
    http://en.wikipedia.org/wiki/Rational_root_theorem .
    (ii) Alternatively, plot the graph of ##y = p(x)## over some ##x##-range, to see roughly where a root lies; that will suggest a factor of ##p(x)##, which you can then verify exactly. (iii) If you are still desperate you can always submit the problem to an on-line solver, such as Wolfram Alpha.
     
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