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Math Help - Calculus 3 proof problem

  1. #1
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    Calculus 3 proof problem

    If f satisfies f(tx) = (t^n)f(x) for all t and some fixed positive integer n, show that:

    gradient f(x) * x = nf(x)



    *Note: x represents a vector
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  2. #2
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    Quote Originally Posted by Drumiester View Post
    If f satisfies f(tx) = (t^n)f(x) for all t and some fixed positive integer n, show that:

    gradient f(x) * x = nf(x)
    Let \mathbf{x} = (x_1,\ldots,x_k) (assuming that the vector is in a k-dimensional space). You are told that f(tx_1,\ldots,tx_k) = t^nf(x_1,\ldots,x_k). Differentiate that equation with respect to t (using the chain rule to differentiate the left-hand side), then put t=1.
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