1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Calculus question

  1. Dec 13, 2004 #1

    Could someone help me with this question please ?

    A set of curves which all pass the origin, have equations :

    y=f3(x)...... where f ' n(x) = fn-1(x) and f1(x) = x^2

    1.) find the expression for fn(x)

    2.) find f2(x) and f3(x)

    I don't know where to begin, especially the first question .


  2. jcsd
  3. Dec 13, 2004 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    How is the derivative of a function related to the function itself? Through the operation of the integral. So

    [tex]f_n'(x) =\frac{df_n}{dx} = f_{n-1}(x) \Leftrightarrow ...[/tex]
    Last edited: Dec 13, 2004
  4. Dec 13, 2004 #3
    Could somebody else explain further please ?
  5. Dec 13, 2004 #4
    Actually quasars tip is totally ok. I would have given the same answer... Just try it...f1 is x² and the derivative of f2 equals f1 = x²...So in order to find f2, just integrate x² with respect to x. You get x³/3...can you move on from here...

  6. Dec 13, 2004 #5


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Assuming you have genuinely been trying to solving the thing for the past 45 minutes, I'll complete the reasoning...

    (Assuming f is continuous,)

    [tex]\Leftrightarrow df_n = f_{n-1}(x)dx \Leftrightarrow \int_0^x df_n = \int_0^x f_{n-1}(x)dx \Leftrightarrow f_n(x) - f_n(0) = \int_0^x f_{n-1}(x)dx \Leftrightarrow f_n(x) - 0 = \int_0^x f_{n-1}(x)dx \Leftrightarrow f_n(x) = \int_0^x f_{n-1}(x)dx[/tex]

    Because if they pass the origin, when x = 0, f = 0.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook