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Simple Calc Problem Need Help

  1. Dec 19, 2008 #1
    1. The problem statement, all variables and given/known data

    4) Let f(x)= ax+(b/x) where a and b are positive constants.
    (a) Find in terms of a and b, the intervals on which f is increasing.
    (b) Find the coordinates of all local maximum and minimum points.
    (c) On what interval(s) is the graph concave up?
    (d) Find any inflection points. Explain your answer.

    3. The attempt at a solution

    I need to take the derivative so it is f'(x)= a-b(x^-2) then I set this equal to zero to find the critical points, but then I'm not sure what value to solve for. X? If I do that I get critical points at +/- [tex]\sqrt{}b/a[/tex]
  2. jcsd
  3. Dec 19, 2008 #2


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    Staff Emeritus
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    If you set a- bx-1 equal to 0, the only thing left to solve for is x! Yes, [itex]x= \sqrt{b/a}[/itex] and [itex]x= -\sqrt{b/a}[/itex] are the critical values of x. What does that tell you about a, b, c, and d?
  4. Dec 19, 2008 #3
    so is the function increasing from (-infinity,-root(b/a)) union (root(b/a),infinity)? Then should I take the second derivative set it equal to zero to find the inflection point
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