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Homework Help: Function and its tangent

  1. Jan 26, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the equation f(x) who's integral is [tex]\int x^{3}[/tex] and has a tangent x+y=0

    2. Relevant equations



    3. The attempt at a solution

    I know that f(x) is 1/4x4+c because of the integral. The tangent is the derivative of f(x) at some point

    i have the equations

    y=x3+c
    y=-x

    but solving these equations gives me two unknowns...
     
  2. jcsd
  3. Jan 26, 2010 #2

    Char. Limit

    User Avatar
    Gold Member

    Well, at what point does x^3 equal negative 1 (the slope of y=-x)
     
  4. Jan 26, 2010 #3

    Mark44

    Staff: Mentor

    What you have written is not very clear. From what I can tell, f(x) = (1/4)x4 + C.

    You're given that f is tangent to the graph y = -x. This means that f'(x) = x3 has to equal -1 (the slope of the line y = -x). It also means that the graph of f has to have a point in common with the line y = -x.
     
  5. Jan 26, 2010 #4
    -1?
    so

    1/4x4+c=1
    1/4(-1)+c=1
    c=3/4

    f(x)= 1/4x4+3/4
     
  6. Jan 26, 2010 #5

    Mark44

    Staff: Mentor

    -1 for what?
    Why 1? You're not explaining what you're doing, which makes it extremely difficult to understand your work.
     
  7. Jan 26, 2010 #6
    Sorry, I was replying to Char. limit's question
     
  8. Jan 27, 2010 #7

    Mark44

    Staff: Mentor

    Can you post the problem exactly as it is worded? I'm having a hard time believing this is what you have actually been given:
    especially the part that says "who's integral is [itex]\int x^{3}[/itex]..."
     
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