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Math Help - Suppose f is differentiable at a.

  1. #1
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    Suppose f is differentiable at a.

    I am still contemplating over this proble, so if anyone is out there who can help me thanks. Suppose that the function f is differentiable at a. Prove (without
    quoting a theorem) that f 2 is differentiable at a.
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  2. #2
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    Quote Originally Posted by Swamifez View Post
    I am still contemplating over this proble, so if anyone is out there who can help me thanks. Suppose that the function f is differentiable at a. Prove (without
    quoting a theorem) that f 2 is differentiable at a.
    What do you mean by f 2?
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  3. #3
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    f squared is what i meant.
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  4. #4
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    f is differentiable at a implies that f'(a) = [f(a+h) - f(a)]/h as h->0
    take g(x) = [f(x)]^2
    therefore lim h->0 [[f(a+h)]^2 - [f(a)]^2 ]/h = f'(a) * [f(a+h)+f(a)]
    and u can easily see that the second bracket is equal to 2*f(a) as h->0
    so the square of f is differentiable at a and the derivative is 2f(a)*f'(a)
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