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Find a formula for a constant function using the mean value theorem

  1. Dec 18, 2009 #1
    1. The problem statement, all variables and given/known data
    Let x ϵ R such that f'(x) = 3x^2. Prove that f(x) = x^3 + c for some c ϵ R using the Mean Value Theorem.

    2. Relevant equations

    3. The attempt at a solution
    I used two functions f(x) and g(x) that have the same derivative namely f'(x). Applying the theorem I am able to work up until f(x) = g(x), I am unsure of where to go from there.
  2. jcsd
  3. Dec 18, 2009 #2
    If you reached the conclusion [tex]f(x) = g(x)[/tex] from only the hypothesis [tex]f'(x) = g'(x)[/tex], something is clearly wrong, since that deduction is false.

    You have a function that's expected to be a constant, namely [tex]f(x) - x^3[/tex]. Work with that.
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