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Math Help - differentiable

  1. #1
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    differentiable

    Def: Let f be a real-valued function defined on an interval I containing the point c, (we allow the possibilty that c is an endpoint of I) we say that f is differentiable at c (or has a derivative at c) if the limit

    lim x->c (f(x) - f(c))/(x-c)
    exists and is finite.

    A) Use definition above to prove that f'(x) = (1/3)^(-2/3) for x is not equal to 0
    B) Show that f is not differentiable at x = 0
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    Quote Originally Posted by learn18 View Post
    Def: Let f be a real-valued function defined on an interval I containing the point c, (we allow the possibilty that c is an endpoint of I) we say that f is differentiable at c (or has a derivative at c) if the limit

    lim x->c (f(x) - f(c))/(x-c)
    exists and is finite.

    A) Use definition above to prove that f'(x) = (1/3)^(-2/3) for x is not equal to 0
    B) Show that f is not differentiable at x = 0
    What function?
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  3. #3
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    the way im reading it, but its prob wrong, is that f can be any real valued function
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    Quote Originally Posted by ThePerfectHacker View Post
    What function?
    Quote Originally Posted by learn18 View Post
    the way im reading it, but its prob wrong, is that f can be any real valued function
    Yes, but we need a specific function for part A. You didn't give it to us.

    -Dan
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  5. #5
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    Im sorry, I must have just completely lost it
    here is the function for a and b

    f(x) = x^(1/3) for x element of R
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    Quote Originally Posted by learn18 View Post
    Im sorry, I must have just completely lost it
    here is the function for a and b

    f(x) = x^(1/3) for x element of R
    I give you a hint that should help.

    [x^(1/3) - a^(1/3)]/ (x-a)

    Multiply the numerator and denominator by,

    x^(2/3) + a^(1/3) * x^(1/3) + a^(2/3)

    This will rationalize the numerator.
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