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Calculus (MVT of Integrals?)

  1. Feb 27, 2007 #1
    1. The problem statement, all variables and given/known data
    Let f be a differentiable function defined for all x>=0 such that f(0)=5 and f(3)=-1. Suppose that for any number b>0, the average value of f(x) on the interval 0<=x<=b is (f(0)+f(b))/x

    a. Find the integral of f(x) from 0 to 3.
    b. Prove that f'(x)=(f(x)-5)/x for all x<0.
    c. Using part b), find f(x)

    2. Relevant equations
    (b-a)(f((ave)x))= the integral of f(x) from a to b

    3. The attempt at a solution
    Part a is easy, I got 6 as my answer. I'm completely at a loss on how to do part b/c. If anyone would at least point me in the right direction, I would greatly appreciate it.
    Last edited: Feb 27, 2007
  2. jcsd
  3. Feb 27, 2007 #2


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    Either you copied out the question wrong or the question asked doesn't make sense.
  4. Feb 27, 2007 #3
    Argh, yes I did copy it wrong. It should be (f(0)+f(b))/2.
  5. Feb 28, 2007 #4


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    Use your "relevant equations" together with the given formula for the average of f over [0,b] to get an equation. Differentiate both sides of the equation.
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