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Math Help - Differentiability implies linearity question

  1. #1
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    Differentiability implies linearity question

    Hello, my problem is:

    Let f: R^m \to R differentiable and f(x/2) = f(x)/2 for all x \in R^m. Prove that f is linear.

    I think the aswer involves the gradient, but I don't know why.
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  2. #2
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    Re: Differentiability implies linearity question

    differentiate the equation, we got f'(x/2)/2=f'(x)/2, so f'(x)=f'(x/2)=...=f'(0) is constant.
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