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Definition of Derivative to Find Constants A, B, and C

  1. Sep 29, 2010 #1
    1. The problem statement, all variables and given/known data
    Ax^2 + Bx + C if neg. infinity < x </= 0
    f(x) =
    x^(3/2) cos (1/x) if 0 <x< pos. infinity

    Use the definition of the derivative to determine all possible values of the constants A, B and C such that f'(0) exists. Cannot use differentiation formulas.

    2. Relevant equations

    definition of the derivative: lim h->0 of (f(a+h) -f(a))/h

    3. The attempt at a solution
    I used the definition of the derivative for Ax_2 + Bx + C and got an answer of B; but what am I supposed to be looking for? Would f'(0) just be B?
    and do I have to do anything with the second part ( x^(3/2) cos 1/x)?
  2. jcsd
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